Despite great improvements of the semiconductor industry in terms of energy efficiency, the computer systems’ energy consumption is constantly growing. Many largely used applications – usually referred to as Recognition, Mining and Synthesis (RMS) applications – are more and more deployed as mobile applications and on Internet of Things (IoT) structures. Therefore, it is mandatory to improve the future silicon devices and architectures on which these applications will run. Inherent resiliency property of RMS applications has been thoroughly investigated over the last few years. This interesting property leads applications to be tolerant to errors, as long as their results remain close enough to the expected ones. Approximate Computing (AxC) , is an emerging computing paradigm which takes advantages of this property. AxC has gained increasing interest in the scientific community in last years. It is based on the intuitive observation that introducing selective relaxation of non-critical specifications may lead to efficiency gains in terms of power consumption, run time, and/or chip area. So far, AxC has been applied on the whole digital system stack, from hardware to application level. This work focuses on approximate integrated circuits (AxICs), which are the result of AxC application at hardware-level. Functional approximation has been successfully applied to integrated circuits (ICs) in order to efficiently design AxICs. Specifically, we focus on testing aspects of functionally approximate ICs. In fact – since approximation changes the functional behavior of ICs – techniques to test them have to be revisited. In fact, some previous works – have shown that circuit approximation brings along some challenges for testing procedures, but also some opportunities. In particular, approximation procedures intrinsically lead the circuit to produce errors, which have to be taken into account in test procedures. Error can be measured according to different error metrics. On the one hand, the occurrence of a defect in the circuit can lead it to produce unexpected catastrophic errors. On the other hand, some defects can be tolerated, when they do not induce errors over a certain threshold. This phenomenon could lead to a yield increase, if properly investigated and managed. To deal with such aspects, conventional test flow should be revisited. Therefore, we introduce Approximation-Aware testing (AxA testing). We identify three main AxA testing phases: (i) AxA fault classification, (ii) AxA test pattern generation and (iii) AxA test set application. Briefly, the first phase has to classify faults into catastrophic and acceptable; the test pattern generation has to produce test vectors able to cover all the catastrophic faults and, at the same time, to leave acceptable faults undetected; finally, the test set application needs to correctly classify AxICs under test into catastrophically faulty, acceptably faulty, fault-free. Only AxICs falling into the first group will be rejected. In this thesis, we thoroughly discuss the three phases of AxA testing, and we present a set of AxA test techniques for approximate circuits. Firstly, we work on the classification of AxIC faults into catastrophic and acceptable according to an error threshold (i.e. the maximum tolerable amount of error). This classification provides two lists of faults (i.e. catastrophic and acceptable). Then, we propose an approximation-aware (ax-aware) Automatic Test Pattern Generation. Obtained test patterns prevent catastrophic failures by detecting catastrophic defects. At the same time, they minimize the detection of acceptable ones. Finally – since the AxIC structure often leads to a yield gain lower than expected – we propose a technique to correctly classify AxICs into “catastrophically faulty”, “acceptably faulty”, “and fault-free”, after the test application. To evaluate the proposed techniques, we perform extensive experiments on state-ofthe-art AxICs.