This chapter explores residual diagnostics and overdispersion in Generalized Linear Models (GLMs), with a focus on logistic and Poisson regressions. Beginning with the definition and visualization of residuals, including binned residual plots and DHARMa diagnostics, it underscores the importance of assessing model fit beyond classical deviance statistics. It then addresses overdispersion, a common violation in GLMs where observed variance exceeds theoretical expectations. Both frequentist (quasi-likelihood, negative binomial, and zero-inflated models) and Bayesian approaches (ZIBB and ZINB) are introduced to flexibly handle overdispersion and excess zeros. Using clinical data from the All of Us study, this chapter provides practical modeling guidance, comparison of model outputs, and insights into the implications of ignoring dispersion and heterogeneity in biomedical research.