We present C-VEM, a scalable library for Virtual Element Methods (VEM) of arbitrary order in 2D and 3D. An overview of the mesh data format, element matrix integration, assemblage and linear solvers implemented is provided. Numerical experiments performed on a wide range of applications are used to illustrate the methodology, and a road-map of how to extend the library with a new application is outlined. The library will be publicly released on https://github.com/.