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HMMHSMM: Inference and Estimation of Hidden Markov Models and Hidden Semi-Markov Models Provides flexible maximum likelihood estimation and inference for Hidden Markov Models (HMMs) and Hidden Semi-Markov Models (HSMMs), as well as the underlying systems in which they operate. The package supports a wide range of observation and dwell-time distributions, offering a flexible modelling framework suitable for diverse practical data. Efficient implementations of the forward-backward and Viterbi algorithms are provided via 'Rcpp' for enhanced computational performance. Additional functionality includes model simulation, residual analysis, non-initialised estimation, local and global decoding, calculation of diverse information criteria, computation of confidence intervals using parametric bootstrap methods, numerical covariance matrix estimation, and comprehensive visualisation functions for interpreting the data-generating processes inferred from the models. Methods follow standard approaches described by Guédon (2003) <<a href="https://doi.org/10.1198%2F1061860032030" target="_top">doi:10.1198/1061860032030</a>>, Zucchini and MacDonald (2009, ISBN:9781584885733), and O'Connell and Højsgaard (2011) <<a href="https://doi.org/10.18637%2Fjss.v039.i04" target="_top">doi:10.18637/jss.v039.i04</a>>. https://CRAN.R-project.org/package=HMMHSMM