The reproductive diversity of extant cartilaginous fishes (class Chondrichthyes) is extraordinarily broad, reflecting more than 400 million years of evolutionary history. Among their many notable reproductive specialisations are viviparity (live-bearing reproduction) and matrotrophy (maternal provision of nutrients during gestation). However, attempts to understand the evolution of these traits have yielded highly discrepant conclusions. Here, we compile and analyse the current knowledge on the evolution of reproductive diversity in Chondrichthyes with particular foci on the frequency, phylogenetic distribution, and directionality of evolutionary changes in their modes of reproduction. To characterise the evolutionary transformations, we amassed the largest empirical data set of reproductive parameters to date covering nearly 800 extant species and analysed it via a comprehensive molecular-based phylogeny. Our phylogenetic reconstructions indicated that the ancestral pattern for Chondrichthyes is 'short single oviparity' (as found in extant holocephalans) in which females lay successive clutches (broods) of one or two eggs. Viviparity has originated at least 12 times, with 10 origins among sharks, one in batoids, and (based on published evidence) another potential origin in a fossil holocephalan. Substantial matrotrophy has evolved at least six times, including one origin of placentotrophy, three separate origins of oophagy (egg ingestion), and two origins of histotrophy (uptake of uterine secretions). In two clades, placentation was replaced by histotrophy. Unlike past reconstructions, our analysis reveals no evidence that viviparity has ever reverted to oviparity in this group. Both viviparity and matrotrophy have arisen by a variety of evolutionary sequences. In addition, the ancestral pattern of oviparity has given rise to three distinct egg-laying patterns that increased clutch (brood) size and/or involved deposition of eggs at advanced stages of development. Geologically, the ancestral oviparous pattern arose in the Paleozoic. Most origins of viviparity and matrotrophy date to the Mesozoic, while a few that are represented at low taxonomic levels are of Cenozoic origin. Coupled with other recent work, this review points the way towards an emerging consensus on reproductive evolution in chondrichthyans while offering a basis for future functional and evolutionary analyses. This review also contributes to conservation efforts by highlighting taxa whose reproductive specialisations reflect distinctive evolutionary trajectories and that deserve special protection and further investigation.