Currently, most editions of The Spanish Tragedy work from the earliest known version, published in 1592. But throughout the seventeenth century, the version most often read and performed was that printed in a 1602 edition. The difference between these two editions is small, consisting of five added segments in the 1602 version.
Three of these additions were simply inserted into the text, and two replaced certain lines in the original text. The places of insertion were as follows: act II, scene v, between line 45 and 46; act III, scene ii, replacing line 65 and part of 66; act III, scene xi, between line 1 and 2; act III, between scene xii and scene xiii; act IV, scene iv, replacing 168 to 190. The additions were extremely popular in their day, and we imagine that this is because the elements of the play they expand upon were those that most impressed audiences of The Spanish Tragedy—Hieronimo's incredible grief and his increasing madness. For example, the first addition portrays Hieronimo going briefly insane after discovering the body of his son. The fourth addition (the longest at over 160 lines and the most famous, frequently referred to as the "painter scene") focuses on Hieronimo's grief and need for justice in much the same way that scene xiii does.
So these sections are valuable in the sense that they provide a hint as to the initial audience reaction to Kyd's play. But editors have become increasingly less fond of the additions, recognizing that their more exuberant, unrestrained style contrasts jarringly with Kyd's refined, formal, and ornate poetry. In the "painter scene", for example, Hieronimo speaks in prose, something he never does anywhere else in the text. One might say this is more naturalistic, but since they were all composed after his death, he had no hand in composing or approving them. Moreover, no new thematic ground or significant plot developments are introduced in the additions. They are merely extra "goodies" for an audience that loved to see people going insane with grief.
But, the additions are undeniably well-written in parts; energetic, emotional, moving (especially the third addition, and its speech about sons). There is much contention as to their authorship, some people even suggesting that Shakespeare wrote them. Traditionally, authorship is assigned to Ben Jonson, though they are very different from Jonson's neoclassical style. In any case, most modern editions allow the reader to decide for themselves whether or not the additions contribute to the play, by printing them if not within the body of the text then at the end of it, indicating where each passage should be added.