For Peter F. Strawson, transcendental arguments were an important part of his philosophical method, referred to as a connective analysis. Both Strawson and his critical commentators have devoted a lot of effort to determining the nature, scope and purpose of those arguments. In this text, I intend, first of all, to reconstruct and characterize the basic elements of transcendental argumentation, specifying its general form, features and purpose. Secondly, I reconstruct some of the most representative examples of this argumentation. Thirdly, I refer to the basic objections against transcendental arguments formulated in the literature. Finally, I point to a few peculiarities in those arguments, commonly omitted by commentators and interpreters. The overall message of the paper is moderately positive: transcendental arguments are a legitimate way of reasoning in philosophy, and in particular, they constitute a comprehensible and well-founded part of Strawson’s connective analysis.