In this chapter we extend the duality results obtained so far to the setting of boundary-driven non-equilibrium systems, i.e., systems driven out of equilibrium via the action of multiple reservoirs where particles can enter and leave the system. We will see that in this context, the processes are no longer self-dual, but dual to processes where the reservoirs are replaced with absorbing sites. In the first section we start with the simplest setting of independent random walkers moving on a one-dimensional chain, in contact with two external reservoirs placed at left and right ends of the system. In Sect. 11.3 we will consider the whole class of interacting particle systems studied in the previous chapters where we add the action of reservoirs. This class includes independent random walkers, symmetric inclusion process and symmetric exclusion process, in their inhomogeneous version, on general graphs and with a general set of reservoirs. For all these models we will prove duality between the process with reservoirs and the process with absorbing boundaries, both with “triangular” and with “orthogonal” duality functions. As applications of these duality results, we will prove existence and uniqueness of the so-called non-equilibrium steady state. We will use the triangular duality to prove properties of the “n-point correlation function”, and we will use the orthogonal duality to obtain information about the multivariate centered moments. In Sect. 11.4 we will see how to add reservoirs for processes with continuous variables. We will focus on two models: the Brownian energy process with reservoirs, where we prove duality with the symmetric inclusion process with absorbing sites, and the deterministic energy process that we will show to be dual to independent random walkers with absorbing sites. Finally we will briefly discuss a continuous-continuous duality property, between continuous models with reservoirs and continuous models with absorbing sites.