We propose the Gaussian-Linear Hidden Markov model (GLHMM), a generalisation of different types of HMMs commonly used in neuroscience. In short, the GLHMM is a general framework where linear regression is used to flexibly parameterise the Gaussian state distribution, thereby accommodating a wide range of uses -- including unsupervised, encoding and decoding models. GLHMM is implemented as a Python toolbox with an emphasis on statistical testing and out-of-sample prediction -- i.e. aimed at finding and characterising brain-behaviour associations. The toolbox uses a stochastic variational inference approach, enabling it to handle large data sets at reasonable computational time. The approach can be applied to several data modalities, including animal recordings or non-brain data, and applied over a broad range of experimental paradigms. For demonstration, we show examples with fMRI, electrocorticography, magnetoencephalography and pupillometry.