Although fixed-effects models for panel data are now widely recognized as powerful tools for longitudinal data analysis, the limitations of these models are not well known. We provide a critical discussion of 12 limitations, including a culture of omission, low statistical power, limited external validity, restricted time periods, measurement error, time invariance, undefined variables, unobserved heterogeneity, erroneous causal inferences, imprecise interpretations of coefficients, imprudent comparisons with cross-sectional models, and questionable contributions vis-à-vis previous work. Instead of discouraging the use of fixed-effects models, we encourage more critical applications of this rigorous and promising methodology. The most important deficiencies—Type II errors, biased coefficients and imprecise standard errors, misleading p values, misguided causal claims, and various theoretical concerns—should be weighed against the likely presence of unobserved heterogeneity in other regression models. Ultimately, we must do a better job of communicating the pitfalls of fixed-effects models to our colleagues and students.