In the presentation, I will talk about different discretization methods for the diffusion equation on polyhedral meshes. I will start with a brief discussion of several well-known approaches, such as finite volumes and divconst. In the main part of the talk, I will speak about new recently developed approach called piece-wise constant approximation. This method has some interesting properties, such as low computational cost and good treatment of thin layers, which makes it suitable for applications arising, for instance, from oil industry. I will show the application of the method to polyhedral meshes consisting of hexahedrons and degenerated hexahedrons, such as prisms, and will demonstrate its competitiveness.