The conductance of a mesoscopic device is usually described in terms o
f the transmission of electrons between electrical contacts. Implicit
in this description is the assumption that contacts can be approximate
d as ideal thermal reservoirs which act solely to thermalise incident
electrons before re-injecting them into the device. We describe two cl
asses of experiment where this assumption is not valid. First, when th
e dissipation in the system is strongly dependent on an external param
eter, such as temperature or magnetic field, the physical position of
the contact may itself depend the parameter. We study this by investig
ating the transport properties of quantum wires with disordered contac
ts. Second, when there is the possibility of some sort of interaction
between the electrons in the contact and those in the device, as we fi
nd in resonant tunnelling from a 2D contact into a 0D state. In both c
ases we find that the conductance properties of the device are strongl
y modified by the nature of the contact.