  Using the combinatorics of the underlying simplicial complex $K$, we give
various upper and lower bounds for the Lusternik-Schnirelmann (LS) category of
moment-angle complexes $\zk$. We describe families of simplicial complexes and
combinatorial operations which allow for a systematic description of the LS
category. In particular, we characterise the LS category of moment-angle
complexes $\zk$ over triangulated $d$-manifolds $K$ for $d\leq 2$, as well as
higher dimension spheres built up via connected sum, join, and vertex doubling
operations. %This characterisation is given in terms of the combinatorics of
$K$, the cup product length of $H^*(\zk)$, as well as a certain Massey
products. We show that the LS category closely relates to vanishing of Massey
products in $H^*(\zk)$ and through this connection we describe first structural
properties of Massey products in moment-angel manifolds. Some of further
applications include calculations of the LS category and the description of
conditions for vanishing of Massey products for moment-angle manifolds over
fullerenes, Pogorelov polytopes and $k$-neighbourly complexes, which double as
important examples of hyperbolic manifolds.
