Approximate computing (AxC) is increasingly emerging as a new design paradigm to produce more efficient computation systems by judiciously reducing the computation quality. In particular, AxC has been successfully applied to integrated circuits (ICs), in the last years. Hence, concerning the test of such new class of ICs, namely approximate ICs (AxICs), new challenges--as well as new opportunities--have emerged. In this survey, we provide a thorough analysis of issues related to test procedures for AxICs and review the state-of-the-art techniques to deal with them. We resort to an illustrative example having the twofold aim of: 1) guiding the reader through the AxIC testing challenges and 2) illustrating the existing solutions to correctly overcome them, while suitably taking advantage of opportunities coming from approximation. We analyze experimentally the most recent testing techniques for AxICs and highlight their mature aspects, as well as their shortcomings. Experimental outcomes show that the testing process for AxIC is not completely mature. Indeed, only under specific conditions existing testing procedures achieve good results.