abstract: We shall first recall the representation theory certain C2 cofinite vertex algebras appearing in logarithmic conformal field theory (joint work with A. Milas). We shall discuss classification of irreducible modules, the structure of Zhu's algebras and the construction of projective modules. We shall show that the representation theory of certain affine vertex algebras are related with these vertex algebras. New explicit realizations of modules for affine Lie algebras and superconformal algebras will be also presented.