"An acrostic is a poem in which the initial letters of each successive line form a word, phrase or pattern." (Oxford Companion to the Bible, p. 6) The acrostic psalms tend to use the twenty-two letters of the Hebrew alphabet. Many of them are now imperfect; that is, each line or stanza no longer uses all the letters in the correct order.
There are nine acrostic psalms: 9-10; 25; 34; 37; 111; 112; 119 and 145. Psalm 119 is the most complete acrostic psalm.
Acrostics tend to be hidden in English translations. The KJV of Psalm 119 marks the stanzas with the Hebrew letter.
ChiasmusChiasmus has been identified in several psalms. I give the general form of them, by verse, here.
Psalm 821
2
3-4
5
6
7
8
Psalm 86
1-4
5-6
7
8-10
11
12-13
14
15
16-17
Psalm 92
1-3
4-6
7
8
9
10-11
11-15
Sources:
The Oxford Bible Commentary
The Oxford Companion to the Bible