This chapter focuses on the quantum Hamiltonian formulation of nonequilibrium processes which, in turn, is based on the master equation. It discusses a few basic facts about Hecke algebras. The chapter shows that the integrability of certain singlespecies reaction–diffusion processes, through their relation to integrable vertex models. It reviews some further methods such as spectral and partial integrability, the free-fermion technique, similarity transformations or diffusion algebras. The chapter shows how the introduced concept of local scale-invariance might become useful in the description of nonequilibrium ageing phenomena. A class of non-equilibrium models which are particularly simple to formulate are the so-called reaction–diffusion processes. The description of reaction–diffusion processes with pair reactions in low dimensions requires a truly microscopic approach beyond kinetic reaction–diffusion equations while these equations may well turn out to be adequate for multi-particle reactions. In trying to extract explicit information on certain reaction–diffusion systems, the integrability of the quantum Hamiltonian H plays a central role.