We consider the problem of tensor factorisation and study it using a generative model. We show how to compute rigorously the mutual information and the Minimal Mean Square Error, and unveil the existence of information theoretic phase transitions. In addition; we also study the behaviour of Approximate Message Passing and show that it achieves the MMSE for a large set of parameters, and, perhaps surprisingly, that the problem is algorithmically easy in a much larger region than previously believed. We also show that it exists a “hard”’ region where AMP fail to reach the MMSE, where we conjecture that no polynomial algorithm will be able to perform a good factorisation.