Molecular clouds are the birthplace of new stars and consist of gas and dust. The dust refers to nanosized grains which provide a surface for molecules to form on. However, the first models used by astrochemists were pure gas-models, using deterministic chemical rate equations (set of coupled ordinary differential equations) and they were able to explain the observed molecular abundancies with partial success. In my talk, I will briefly motivate the study of molecules in space and the advantage of stochastic methods to model molecule formation. The latter has everything to do with the incorporation of the dust grain surface chemistry in the models. I will focus on a class of stochastic simulation methods that have become known as kinetic Monte Carlo (KMC) methods. After outlining the theory behind the (standard) KMC approach using the formation of H2 as an example, I will go over some KMC algorithms as implemented in our Theoretical & Computational Chemistry group. Next, I will discuss the challenges we face using the KMC method with the simulation of molecular chemistry on dust grain surfaces. Finally, I will pose some mathematical questions that we have, regarding the different implementations of the KMC method and stochastic simulation in general.