This review article delves into the study of low-mass exoplanets: super-Earths, mini-Neptunes and the new categories within and between that we are starting to discover. We provide an overview of current exoplanet observational capabilities, their limitations, and what they are allowing us to learn about low-mass planets. We briefly summarize the most important aspects of planet formation, with an emphasis on processes that may be testable with small exoplanets, in particular those that affect their composition. We also describe the observed compositional diversity of low-mass exoplanets and what it teaches us about planet formation pathways. We finish this review summarizing the study of the composition of small exoplanets during the very last stage of stellar evolution, by studying white dwarfs. This review is written as the JWST is making its first contributions to small planet characterization, rapidly opening new lines of inquiry.

50 pages, 9 figures