The topic of this master's thesis is modeling of diffusion of neurotransmitters in the extracellular space (ECS) of the central nervous system (CNS). In the models presented here diffusion will be affected by the binding of neurotransmitters to receptors or transporters and by the glial sheath around the synaptic cleft.I begin this thesis in section 2 by giving a definition of diffusion. In section 3 I give a short introduction to the biological background needed here. I emphasize two types of signal transmission in the CNS, wire and volume transmission, that depend on diffusion of neurotransmitters. In section 4 I present the diffusion equation and different boundary conditions that arise where receptors and transporters are located. In section 5 I explain how to find numerical solutions to such diffusion problems using the finite element (FEM) and Crank- Nicolson method. Thereafter, in section 6 and 7, I present several models in one and two dimensions. In section 8 I consider the models potential of explaining different phenomena in volume transmission such as crosstalk between neurons. In section 9 I prove characteristics of the numerical solutions found using the FEM and Crank- Nicolson method.