  We review some recent progress in quantum field theory in non-commutative
space, focusing onto the fuzzy sphere as a non-perturbative regularisation
scheme. We first introduce the basic formalism, and discuss the limits
corresponding to different commutative or non-commutative spaces. We present
some of the theories which have been investigated in this framework, with a
particular attention to the scalar model. Then we comment on the results
recently obtained from Monte Carlo simulations, and show a preview of new
numerical data, which are consistent with the expected transition between two
phases characterised by the topology of the support of a matrix eigenvalue
distribution.
