The chain mapping technique refers to a general approach where a unitary transformation enables to map a continuum to an infinite but discrete set. Applied to the system-environment interaction it enables to map a system interacting with a continuum of independent modes to a system interacting with a single mode of a discrete but interacting environment. This change of ‘topology’ enables the direct use of matrix product states to describe the full state of the system and the environment. In this chapter, the usual chain mapping is derived, as well as its recent extensions to finite-temperature problems, and systems with an explicit spatial structure. The connection between finite-temperature chain mapping and the thermofields approach is also discussed.