Representations of W-algebras with two generators and new rational models

In conformal field theory we investigate the representations of recently discovered W-algebras with a single generator in addition to the Virasoro field. We show that many of these W-algebras have only a finite number of highest-weight representations. We describe methods for the classification and give complete lists. In a sporadic case we determine characters and fusion rules. Different methods are used for W-algebras with continuously variable and for those with fixed central extension.