The Zero Range Process is an important example of particle movements in physics. It models particles jumping on a finite set, which surprisingly results in independent occupation numbers in the limit. We will give an overview of Large Deviations in the Zero Range Process and present some important results that arise in the chosen setting of heavy tailed occupation numbers. This gives rise to some related theory like the Catastrophe Principle and the Large Deviations Principle which we will also give a brief introduction to.