In this thesis we aim to create a unified framework for the implementation and analysis of virtual element spaces. The approach we take for the virtual element discretisation allows us to easily construct vector field spaces as well as consider both variable coefficient and nonlinear problems. On top of this, the approach can be integrated more readily into existing finite element software packages. These are significant advantages of the method we present and something that has not been easy to achieve within the original virtual element setting. We exploit these key advantages in this thesis. In particular, we present a straightforward and generic way to define the projection operators, which form a crucial part of the virtual element discretisation, for a wide range of problems. We demonstrate how to build Hm-conforming for m = 1, 2 and nonconforming spaces as well as divergence and curl free spaces. All of which have been implemented in the open source Dune software framework as part of the Dune-Fem module. As a consequence of the projection approach taken in our framework, we are able to carry out a priori error analysis for higher order approximations of the following fourth-order problems: a general linear fourth-order PDE with non-constant coefficients; a singular perturbation problem; and the nonlinear time-dependent Cahn-Hilliard equation. Furthermore, we showcase the versatility of the projection approach with the introduction of a novel nonconforming scheme for the singular perturbation problem. The modified nonconforming method is uniformly convergent with respect to the perturbation parameter and unlike modifications in the literature, does not require an enlargement of the space. Numerical tests are carried out to verify the theoretical results.