It is clear that the Torah commanded animal sacrifices to be made. It is also clear that the Tanakh (i.e. the "Old Testament") states that HaShem does not desire them. How can both be true? Rabbinic authorities differ on this subject. Here is a sampling of their discussions followed by my thoughts on the subject:

--- Rashi (1040-1103) indicated that God did not want the Israelites to bring sacrifices in the first place; he says it was their choice. He bases this on the haphtorah (portion from the Prophets) read on Shabbat when the book of Leviticus is read, on the subject of sacrifices:

I have not burdened thee with a meal-offering, Nor wearied thee with frankincense. (Isaiah 43:23)

--- David Kimhi (1160-1235) goes farther and says that the sacrifices were voluntary. He determined this from the words of Jeremiah:

For I spoke not unto your fathers, nor commanded them on the day that I brought them out of the land of Egypt, concerning burnt-offerings or sacrifices; but this thing I commanded them, saying, "Obey my voice, and I will be your God, and ye shall be my people; and walk ye in all the ways that I have commanded you, that it may be well unto you. (Jeremiah 7:22-23)

Kimhi's view goes too far and is not harmonious with Torah in my opinion. Rambam disagrees with him:

--- Rambam (aka Maimonides) suggests that one reason for the animal offerings was to wean the People of Israel away from the pagan worship of animals. He explains that the ancient Egyptians and others viewed animals as "herds of deities;" thus, the People of Israel were commanded to take the very animals the Egyptians worshiped and offer them to HaShem (Guide to the Perplexed 3:46, cited in the commentary of the Ramban -- i.e. Nachmanides -- on Leviticus 1:9).

Rambam also notes on this point:

-- In the Mishneh Torah (Hilchos Beis HaBechinrah 2:2), citing the ancient tradition that Adam, Cain, and Abel all brought offerings to the site of the then and now future Holy Temple. Although they had a vegetarian diet, Adam and Abel brought animal offerings to HaShem. According to the Talmud, the animal sacrifice made by Adam was an ox (Avodah Zarah 8:a). The Torah states that Abel "brought from the firstlings of his flock and from the choicest" (Genesis 4:4). These individuals lived in the age before the pagan worship of animals emerged; thus (Rambam concludes) one cannot say that the reason for their offerings was to wean themselves from the pagan worship of animals! He seems to have changed his mind, or was perhaps re-examining the subject from a different perspective.

--- Rambam also writes in the Mishneh Torah that in the Olam Haba or messianic age, once the Temple has been rebuilt, we will once again bring the offerings "according to all the particulars mentioned in the Torah" (Hilchos Melachim 11:1) which will include the animal sacrifices. During the messianic age all forms of idolatry will be abolished because everyone will be united in service to the One Creator. The reason for the Temple offerings in our present age cannot therefore be because of a need to wean people from pagan practices, because in the Olam Habah they will resume even though "the earth will be filled with the knowledge of the Lord" (Isaiah 11:9).

However this conclusion is not accepted by all authorities:

---- The Jewish philosopher Isaac ben Judah Abrabanel (1437-1508) disagrees with Rambam here. He cites a Midrash indicating that the Jews had become accustomed to sacrifices in Egypt. In order to feel they were appeasing the Creator they believed they needed to make blood sacrifices. To wean them from these idolatrous practices (whether the sacrifices were as god-animals or merely as animal sacrifices is not specified in his comments), God "tolerated" the sacrifices but commanded that they be offered in one central sanctuary. Obviously intending that one day the people would discard the rites.

---Rabbi J. H. Hertz, the late chief rabbi of England, explains this last point, saying that if Moses had not instituted the kind of sacrifices they were used to, which were admitted by all to have been the universal expression of religious observance, his mission would have failed and Judaism would have disappeared. With the destruction of the Temple, the rabbis began teaching the people that prayer and good deeds took the place of sacrifice. This was already understood by many Jews but after 70 CE it became the established Jewish understanding.

-- Rav Kook also differs from Rambam on this point and taught that in the Olam Haba human conduct will have improved to such a degree that animal sacrifices will no longer be necessary to atone for sins. Implicit in this is that there was a consciousness connection to the ancient sacrifice supporting the idea of weening the people away from idolatry. There will only be non-animal sacrifices to express thanks to God in the Olam Haba according to Rav Kook and many other respected authorities.

It is informative that non-biblical sacrifices sometimes included human sacrifices, which is why (or least one of the reasons why) HaShem ordered Avraham to sacrifice his son Isaac. When the angel stayed his hand both father and son, who were willing to comply with whatever HaShem required, understood that HaShem will not accept those types of sacrifices. This truth was passed down through Isaac, Jacob and their descendents, the Jewish people and human sacrifice was forbidden as an abomination. Arguably the sacrifice of animals took more time to stop because they were more universally practiced and most people were not as spiritually attuned as Avraham and Isaac.

Once the Temple was destroyed in 70 CE all sacrifices ceased. Since then Jews rely Torah study and observance and acts of kindness and these must be rooted firmly in emunah (active faith) that HaShem accepts the sacrifices of Torah study and praise.

Jeremiah 33:10 Thus saith the LORD; Again there shall be heard in this place, which ye say shall be desolate without man and without beast, even in the cities of Judah, and in the streets of Jerusalem, that are desolate, without man, and without inhabitant, and without beast,
33:11 The voice of joy, and the voice of gladness, the voice of the bridegroom, and the voice of the bride, the voice of them that shall say, Praise the LORD of hosts: for the LORD is good; for his mercy endureth for ever: and of them that shall bring the sacrifice of praise into the house of the LORD. For I will cause to return the captivity of the land, as at the first, saith the LORD.

So, I think we can confidently conclude that HaShem required animal sacrifices (i.e. that they were not optional, according to my reading of the Torah) for our spiritual and cultural development, with the intention of elevating the human consciousness to the point that we could conceive of redemption as the intentional attaching of ourselves to HaShem, with emuna (active faith) and kavanah (intention), through the deeper realizations revealed through Torah study and observance. Exactly how and why blood sacrifices were chosen by HaShem (and MAY be again once the Temple is rebuilt according to the Rambam and others) is unclear, but seems to be directly related to the human (and Pagan) invention of animal sacrifice. By 70 CE the people had been "weened" off of these rites.

I agree with what I think is the majority opinion of the sages that in the Olam Haba, once the Temple is rebuilt, only thanksgiving (grain) offerings will be made. Time will tell.

The important thing in any event is that:

What I want is mercy, not sacrifice, (Hosea 6:6)

As Rebbe Nachman of Breslov explained:

"The only way to know God is through complete faith.
Only faith can bring you to true knowledge and perception of God's greatness:

"And I will betroth you to Me with faith, and you shall know God!-- " [Hosea 2:22]

A few additional verses to consider:

To what purpose is the multitude of your sacrifices unto Me?" sayeth the Lord. "I am full of the burnt offerings of rams, and the fat of fed beasts; and I delight not in the blood of bullocks, or of lambs or of he-goats...bring no more vain oblations.... Your new moon and your appointed feasts my soul hateth;...and when ye spread forth your hands, I will hide mine eyes from you; yea, when ye make many prayers, I will not hear; your hands are full of blood. (Isa. 1:11-16)

I hate, I despise your feasts, and I will take no delight in your solemn assemblies. Yea, though you offer me burnt-offerings and your meal offerings, I will not accept them neither will I regard the peace-offerings of your fat beasts. Take thou away from me the noise of thy song; and let Me not hear the melody of thy psalteries. But let justice well up as waters, and righteousness as a mighty stream. (Amos 5:21-4)

For I spoke not unto your fathers, nor commanded them on the day that I brought them out of the land of Egypt, concerning burnt-offerings or sacrifices; but this thing I commanded them, saying, "Obey my voice, and I will be your God, and ye shall be my people; and walk ye in all the ways that I have commanded you, that it may be well unto you. (Jeremiah 7:22-23)

Micah 6:6 With what shall I come before the Lord, bow before the Most High God? Shall I come before Him with burnt offerings, with yearling calves?
6:7 Will the Lord be pleased with thousands of rams, with myriad streams of oil? Shall I give my firstborn for my transgression, the fruit of my body for the sin of my soul?
6:8 He has told you, O man, what is good, and what the Lord demands of you; but to do justice, to love loving-kindness, and to walk discreetly with your God.

Consider Rashi on verse 8:

and to walk discreetly: Jonathan renders: Walk discreetly in the fear of your God. Another explanation: And walk discreetly. The standard of flesh and blood is not like the standard of the Holy One, blessed be He. The standard of flesh and blood is: If one man embarrasses his fellow and comes to placate him, the fellow says to him, "I will not accept your apology until so and so and so and so, before whom you disgraced me, come." But the Holy One, blessed be He, desires only that the man's return to Him be between the two of them. [from Pesikta d'Rav Kahana 163b]

For a direct statemnt on this let's look at Leviticus Rabbah 9:7:

All sacrifices, except thankofferings, will be abolished in future; and even should prayer be abolished, that portion thereof which comes under Praises will not be abolished.

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I relied heavily on the following sources for this piece:

The Jewish Virtual Library
ShemaYisrael.com

* Rabbi Shlomo Nachman © June 10.2014 (last updated April 27, 23017)
AllFaith.com
LearnEmunah.com
BeitEmunah.com