W-algebras are introduced as central objects in 2-dimensional conformal field theory. Beyond their significance in physics, they also appear in various mathematical contexts, including representation theory and partial differential equations. In this talk, we mainly focus on the smallest yet most important examples of W-algebras, the Virasoro vertex algebras. We review their definition and explore how they can be discovered in various mathematical areas. We then give a brief introduction to W-algebras generalizing the observations for Virasoro vertex algebras.