  We discuss our recent results on the representation theory of
$\mathcal{W}$--algebras relevant to Logarithmic Conformal Field Theory. First
we explain some general constructions of $\mathcal{W}$-algebras coming from
screening operators. Then we review the results on $C_2$--cofiniteness, the
structure of Zhu's algebras, and the existence of logarithmic modules for
triplet vertex algebras. We propose some conjectures and open problems which
put the theory of triplet vertex algebras into a broader context. New
realizations of logarithmic modules for $\mathcal{W}$-algebras defined via
screenings are also presented.
