Bartolucci et al. (Test, 2014) provide a nice showcase of the flexibility of latent Markov models for longitudinal data. Indeed, their list of applications is impressive and includes a wide variety of models, with covariates to model transitions between latent states and direct effects on the observations, such that the model becomes a latent Markov regression model, and models for multivariate data, to mention but a few. Bartolucci et al. also briefly discuss the relationship between latent Markov models and hidden Markov models. These models share their basic assumptions, but were developed with different objectives in mind: the latent Markov model is aimed at longitudinal data, whereas the hidden Markov model is aimed at modeling time-series data. As a result of this difference in focus, different estimation and inference methods have been developed, which each have their strengths and weaknesses. Surprisingly, the literatures on latent and hidden Markov models have remained largely separate. We believe that a marriage between these literatures can provide even greater flexibility to this modeling framework than each of them can muster separately.