The main part of Pesukei d’Zimrah is the last six chapters in the book of Psalms, the most significant being the first, “Tehillah L’David” (Psalm 145). One who recites it three times daily is ensured a place in the World to Come, both because the praises in that Psalm are organized according to the order of the alef-bet, and because it mentions the important verse, “Pote’ach et Yadecha…,” “You open Your hand and satisfy the desire of every living being” (Berachot 4b). It is customary to recite the verse “Ashrei” before it, therefore the Psalm is generally referred to as Ashrei.
Afterwards, we say the five Psalms which start and end with the word “Halleluyah,” about which Rabbi Yossi says, “May my portion be among those who complete the Hallel every day” (Shabbat 118b).
During the era of the Savora’im (after the Amora’im), the recital of “Hodu” (Chronicles I 16:8-36) was instituted, which is the song and praise that King David recited as he returned the Ark of God from the captivity of the Philistines to the tent of the Tabernacle. Later, in the Temple, half of this praise would be recited while offering the morning Tamid and the other half when bringing the Tamid of the afternoon (Beit Yosef, Orach Chaim 50). According to Nusach Ashkenaz, Hodu is said after Baruch She’amar so that all the songs of praise and exaltation are included within the berachot of Pesukei d’Zimrah (Tur, Orach Chaim 51). According to Nusach Sephard, Hodu is said before Baruch She’amar because it is a continuation of the recital of the Tamid offering (Eshkol, Kolbo).
The Savora’im also instituted (Masechet Sofrim 17:11) the recital of a compilation of verses before Ashrei that start with Yehi Chevod. These verses possess a strengthening of one’s faith in Hashem and in the redemption of Israel. The Ari explains the deeper, mystical meanings of this Psalms’ enigmatic words (Kaf HaChaim 51:13).
After that, during the time of the Geonim, it became customary to add more Psalms and verses to Pesukei d’Zimrah. They established saying “Mizmor L’Todah” (Psalm 100). Chazal say that in the future, all songs will be nullified with the exception of this one (Vayikra Rabbah 9:7). Therefore, it is proper to recite it with a melody. It is not said on Shabbatot and festivals; instead, “Mizmor Shir L’Yom HaShabbat” (Psalm 92) is recited. According to the Ashkenazic minhag, Mizmor L’Todah is recited to correspond to the Todah (thanksgiving) offering which contained chametz (leavened bread). For that reason this Psalm is not recited on Erev Pesach, Chol HaMo’ed Pesach, and Erev Yom Kippur, since the Todah offering is not brought on those days because of the prohibition of chametz, or the obligation to fast. However, the Sephardim do recite it on those days because according to the Sephardic minhag, it does not correspond to the Todah offering; rather its fundamental purpose is to praise and express thanks (Beit Yosef and Rama 51:8).
The main parts of Pesukei d’Zimrah are taken from the songs of David, as we say in the wording of Baruch She’amar, “Through the songs of David, Your servant, we will extol You.” Nevertheless, in the period of the Geonim, there were those who had the custom to add verses from the Torah and from the book of Nehemiah, such as Vayevarech David (Chronicles I 29:10-13 and Nehemiah 9:6-11), and Az Yashir (Song at the Sea), that Moshe and the nation of Israel sang to Hashem (Exodus 15:1-18). By the end of the era of the Rishonim everyone became accustomed to saying them.
. Regarding Tehillah L’David (Ashrei): Talmidei Rabbeinu Yonah (23a) write that the essence of the institution to recite Pesukei d’Zimrah is for Tehillah L’David, based on the Gemara in Berachot 4b. The Rosh, chapter 5:6 writes, “In addition to that Psalm, the Chachamim instituted reciting [the remaining Psalms] until the end of the book of Psalms.”What was Rabbi Yossi referring to when he said (Shabbat 118b), “May my portion be among those who complete the Hallel, [meaning Pesukei d’Zimrah,] every day”? According to the Rif, Rosh, and Tur, he was referring to the last six Psalms, from Tehillah L’David until the end of the book of Psalms (Psalms 145-150). So it is written in Masechet Sofrim 17:11. However, Rashi interprets that Rabbi Yossi was discussing the two Psalms that start with “Halleluyah Hallelu” (Psalms 148 and 150). These opinions are brought by the Beit Yosef, end of section 50. Therefore, a distinction is made regarding the level of importance between the two Psalms that start with “Halleluyah Hallelu” and those that only begin with the word “Halleluyah.
In Masechet Sofrim 17:11 (which was redacted in Israel at the end of the period of the Savora’im), it is mentioned that Yehi Chevod, Hodu LaHashem, and the last six Psalms are recited. Later, in the time of the Geonim, it is recorded that we recite Mizmor L’Todah and the passages from Vayevarech David through Az Yashir (just as the Tur Orach Chaim 51 writes, that this is an enactment of the Geonim). Similarly, the Psalms that are added on Shabbat are mentioned in Seder Rav Amram Gaon. However, regarding Az Yashir, which is not one of the songs of David, the Rambam writes (Tefillah 7:13) that some are accustomed to saying it and others are not, each person according to his custom. Sefer HaManhig writes that it is not proper to skip the praise of the first redemption. The verses, “Baruch Hashem l’olam amen v’amen” etc. that are recited after the Halleluyot are originally mentioned by the Roke’ach (who was among the Rishonim of Ashkenaz). Abudraham (the Sephardi) presents a reason – because they are verses that conclude the book of Psalms. Mizmor L’Todah is mentioned in Orchot Chaim (one of the Rishonim). Three hundred years ago, Mizmor Shir Chanukat HaBayit was added to the siddur. Before then, it was only recited on Chanukah. In the Mikdash, it was recited when bikurim (first fruits) were brought (Bikurim 3:4).