This chapter is organized as follows. First, we present some theoretical bases behind spectral discretizations in Sect. 8.1. An application to a problem stemming from the building physics is given in Sect. 8.3. Finally, we give some indications for the further reading in Sect. 8.4. This document contains also a certain number of Appendices directly or indirectly related to spectral methods. For instance, in Appendix 8.5 we give some useful identities about Tchebyshev polynomials and in Appendix 8.6 we give some flavour of Trefftz methods, which are essentially forgotten nowadays. Finally, we prepared also an Appendix 8.7 devoted to the Monte–Carlo methods to simulate numerically diffusion processes.