Finite Element Methods (FEM) are generally constructed based on so called finite element triples (K,B,L). Here K is an element in the grid   (e.g., a triangle), B is the basis of some finite dimensional space   (e.g., a set of polynomials), and L is a set of functionals with |L| = |B|  (e.g., the evaluation of functions on a set of Lagrange points).   The set L are called local degrees of freedom (dofs). Often the aim in the  construction of finite element spaces V_h is to achieve some level of   conformity, i.e., guaranteeing that V_h is a subset of some function space  V. Typical spaces are conforming with V=H^1. Achieving conformity with   V=H^2 or V=H(div) is a lot more challenging. For example, the lowest order   finite element on triangles which leads to V_h being H^2 conforming   requires the use of polynomials of order 5 locally (without using a   piecewise definition). Also changing K from triangles to quadrilaterals  requires defining a complete new set of basis function B and dofs L.  Often a suitable choice for L is not the problem but defining a suitable B  can be challenging.   The Virtual Element Method (VEM) is a recent approach to define a wide   range of spaces on general element shapes including general polygons.  In this talk we will provide a description of the virtual element spaces   which shows that it can be considered to be a direct extension of the FEM   constructing approach. The approach uses a fixed B on each element   independent of the choice of L thus avoiding the problem described above.   We introduce a VEM tuple and describe how that can  be used to define the local spaces. We will focus our presentation on spaces  which can be used to solve forth order problems but will also demonstrate  how the approach can be used to construct other spaces, i.e., divergence   free spaces for fluid dynamics problems.   We will show how this approach simplifies the implementation of VEM methods  within existing FEM codes and discuss a-priori error analysis and numerical  experiments for linear forth order problems with varying coefficients.