Approximate Computing (AxC) is based on the observation that a significant class of applications can inherently tolerate a certain amount of errors (i.e., the output quality is still acceptable to the user). AxC exploits this characteristic in order to apply selective approximations or occasional relaxations of the specifications. The benefit is a significant gain in energy efficiency and area reduction for Integrated Circuits (ICs). During the mission-mode, the IC can be affected by faults caused by environmental perturbations (e.g., radiations, electromagnetic interference), or aging-related phenomena. These faults may be propagated through the IC structure to the outputs and thus lead to observable errors. These errors (due to faults) may worsen the accuracy reduction - already introduced by the AxC - and possibly lead it to become unacceptable. This paper aims at investigating the challenges and the opportunities related to the test of AxC ICs.