Excitable systems are often modelled using reaction-diffusion equations with kinetic terms of varying complexity. The solutions of such reaction-diffusion systems are characterized by many different time and length scales. In the present talk, I will discuss the classical Hodgkin-Huxley (HH) model as an example of excitability, and will explain the problem of the different time and space scales in systems like the HH model. Then, I will describe the purpose of my research, which is focused on the numerical simulation of excitable systems. More specifically, my research work is directed towards the development of spectral methods for the resolution of the fast and slow dynamics with high accuracy and low computational cost.