Alliteration is a characteristic of much Old English verse (such as Beowulf, which includes verses like "feasceaft funden; he þæs frofre gebad, / weox under wolcnum, weorþ-myndum þah," alliterating "f" in the first line and "w" in the second) and some Middle English (such as Sir Gawain and the Green Knight, which begins, "Siþen þe sege and þe assaut watz sesed at Troye / The borgh brittened and brent to brondez and askez, / The tulk þat þe trammes of tresoun þer wroght," alliterating "s," "b," and "t" respectively). In verse since the Renaissance it tends to be used less systematically, but it's still common.
Note: This guide is still in the early stages of development.
Three question marks mean I have to write more on the subject. Bear with me.