Anick conjectured the following after localisation at any sufficiently large prime - after looping, any finite, simply connected CW complex is homotopy equivalent to a finite type product of spheres, loops on spheres, and a list of well studied torsion spaces defined by Cohen, Moore and Neisendorfer. We study this question in the context of moment-angle complexes, a central object in toric topology which are indexed by simplicial complexes. Recently, much work has been done to find families of simplicial complexes for which Anick's conjecture holds integrally. In this talk, I will survey what is known, and show that the loop space of any moment-angle complex is homotopy equivalent to a product of looped spheres after localisation away from a finite set of primes. Using this case, we can also show that Anick's conjecture holds for a much wider family of polyhedral products, as well as quasitoric manifolds and simply connected toric orbifolds. This is joint work with Fedor Vylegzhanin.