  Statistical models that involve latent Markovian state processes have become
immensely popular tools for analysing time series and other sequential data.
However, the plethora of model formulations, the inconsistent use of
terminology, and the various inferential approaches and software packages can
be overwhelming to practitioners, especially when they are new to this area.
With this review-like paper, we thus aim to provide guidance for both
statisticians and practitioners working with latent Markov models by offering a
unifying view on what otherwise are often considered separate model classes,
from hidden Markov models over state-space models to Markov-modulated Poisson
processes. In particular, we provide a roadmap for identifying a suitable
latent Markov model formulation given the data to be analysed. Furthermore, we
emphasise that it is key to applied work with any of these model classes to
understand how recursive techniques exploiting the models' dependence structure
can be used for inference. The R package LaMa adapts this unified view and
provides an easy-to-use framework for very fast (C++ based) evaluation of the
likelihood of any of the models discussed in this paper, allowing users to
tailor a latent Markov model to their data using a Lego-type approach.
