When instruments are weakly correlated with endogenous regressors, conventional methods for instrumental variables estimation and inference become unreliable. A large literature in econometrics develops procedures for detecting weak instruments and constructing robust condence sets, but many of the results in this literature are limited to settings with independent and homoskedastic data, while data encountered in practice frequently violate these assumptions. We review the literature on weak instruments in linear IV regression with an emphasis on results for non-homoskedastic (heteroskedastic, serially correlated, or clustered) data. To assess the practical importance of weak instruments, we also report tabulations and simulations based on a survey of papers published in the American Economic Review from 2014 to 2018 that use instrumental variables. These results suggest that weak instruments remain an important issue for empirical practice, and that there are simple steps researchers can take to better handle weak instruments in applications.