We survey the recent literature on the effects of retirement on cognitive functioning at older ages. We describe results from studies using similar data sets (HRS, SHARE and ELSA), definitions of cognition, and instruments to capture causal effects. The studies yield widely varying results. Most papers find that being retired leads to a decline of cognition, controlling for different specifications of age functions and other covariates. However, richer specifications using fixed effects, dynamic specifications, or alternative specifications of instrumental variables often lead to large changes in the size and significance of the estimated effects. We replicate several of these results using the same data sets. We discuss the factors that are likely causing the differences across specifications, including endogeneity of right hand side variables, and heterogeneity across gender, occupation or skill levels.