We review special issues in multiplicity adjustment where the sampling distributions are discrete. These include (1) incorporating discreteness into the multiplicity adjustments, (2) incorporating correlations versus using Bonferroni or independence-based approximations, and (3) using discrete tails in two-sided tests. Incorporating discrete characteristics can greatly improve the power of the tests that maintain a given familywise error rate. Use of correlations also can improve the power, but it is shown that independence-based multiplicity adjustment is not necessarily a conservative procedure. Exact methods that incorporate discreteness and correlations are generally recommended.