Recent years have seen a surge of interest in "increments" among students of conversational interaction. This article first outlines "incrementing" as an analytical problem (i.e., as turn constructional unit [TCU] extensions) by tracing its origins back to Sacks, Schegloff, and Jefferson's (1974) famous turn-taking article. Then, the article summarizes and reviews Schegloff's recent publications and presentations, which revisited this problem, as well as contributions on the same theme by scholars using data from a variety of languages and settings. It is suggested that authors have generally focused their analytic attention on utterances that contain structural "oddities" (i.e., oddities relative to the "canonical" structures of particular languages), which could, and do, vary tremendously across languages. A general account of TCU extensions can only be built on the basis of more data from a larger variety of languages, and it must be typologically informed.