Hidden tree Markov models allow learning distributions for tree structured data while being interpretable as nondeterministic automata. We provide a concise summary of the main approaches in literature, focusing in particular on the causality assumptions introduced by the choice of a specic tree visit direction. We will then sketch a novel non-parametric generalization of the bottom-up hidden tree Markov model with its interpretation as a nondeterministic tree automaton with innite states.