Subgroup analyses are commonly performed in the clinical trial setting with the purpose of illustrating that the treatment effect was consistent across different patient characteristics or identifying characteristics that should be targeted for treatment. There are statistical issues involved in performing subgroup analyses, however. These have been given considerable attention in the literature for analyses where subgroups are defined by a pre-randomization feature. Although subgroup analyses are often performed with subgroups defined by a post-randomization feature--including analyses that estimate the treatment effect among compliers--discussion of these analyses has been neglected in the clinical literature. Such analyses pose a high risk of presenting biased descriptions of treatment effects. We summarize the challenges of doing all types of subgroup analyses described in the literature. In particular, we emphasize issues with post-randomization subgroup analyses. Finally, we provide guidelines on how to proceed across the spectrum of subgroup analyses.