  We investigate some topological properties, in particular formality, of
compact Sasakian manifolds. Answering some questions raised by Boyer and
Galicki, we prove that all higher (than three) Massey products on any compact
Sasakian manifold vanish. Hence, higher Massey products do obstruct Sasakian
structures. Using this we produce a method of constructing simply connected
K-contact non-Sasakian manifolds. On the other hand, for every $n \geq 3$, we
exhibit the first examples of simply connected compact Sasakian manifolds of
dimension $2n + 1$ which are non-formal. They are non-formal because they have
a non-zero triple Massey product. We also prove that arithmetic lattices in
some simple Lie groups cannot be the fundamental group of a compact Sasakian
manifold.

Differential Geometry;Algebraic Topology