Problems in plasma physics are rich in geometric structure. This is especially true when considering kinetic models (ones which describe the evolution of a probability density function for the charged particles, together with the electromagnetic fields, e.g. the Vlasov--Poisson or Vlasov--Maxwell equations) as they possess infinite-dimensional Hamiltonian / Poisson structure. Exploiting this geometric structure has led to the development of advanced numerical methods for solving (non-dissipative) kinetic problems very accurately.  Issues arise, however, when one is interested in adding collisions to such models, as collisions are dissipative and do not fit into the Hamiltonian structure of the problem. This can be resolved through the use of the metriplectic formulation of Morrison, which is a geometric way of describing Hamiltonian systems with dissipation. This formulation can also be utilised to construct accurate numerical discretisations when modelling such coupled systems, which is a much more recent topic of study.  In this talk, I will introduce the relevant plasma physics models and their geometric structure. I will then present the metriplectic formulation, and detail how it can be used to describe Hamiltonian systems with dissipation. Finally, I will describe how the metriplectic structure of collision operators can be used to construct discretisations in a way that preserves the quantities of interest using relevant examples.