This chapter outlines how hidden Markov models (HMM) can be used to model longitudinal data, known in the econometric literature as panel data. In some applications the component series are assumed to be driven by the same sequence of states. An application of this type is the HMM for daily precipitation occurrence at multiple sites described by Walter Zucchini and P. Guttorp. HMMs for longitudinal data with fixed effects can involve a large number of parameters, especially when the number of subjects, K, is large. HMMs offer the means to accommodate such distinctions and similarities. Subject-specific covariates, if available, can explain some of the differences between subjects. Covariate information is easily incorporated into HMMs. In general, the use of random effects is a convenient way to reduce the number of parameters that need to be estimated, especially when the number of subjects is large.