As cyber-attacks grow in frequency and complexity every year, digital systems critically rely on complex security mechanisms. With Approximate Computing (AxC) reaching maturity for practical application, the long-neglected security implications of this paradigm must be understood and addressed. This chapter provides an overview of both: security threats potentially stemming from AxC hardware blocks, and opportunities for better security constructions based on AxC. Concerning the threats, we will discuss security issues related with design and manufacturing (reverse engineering, hardware Trojans, counterfeiting, and piracy) of approximate circuits and with their operation (side channel, covert-channel, and fault-injection attacks). For each threat, we will discuss the consequences of the transition from classical to approximate circuits. We will then present two promising applications of AxC technology in homomorphic encryption and in defending neural networks against adversarial attacks. Approximated homomorphic encryption can reduce the computational overhead of large-scale computations performed in the encrypted domain. We will provide an implementation angle for scenarios such as cloud computing or machine learning/AI, where the improved efficiency of the computation is particularly beneficial. Then, we will discuss how stochastic computing (a type of AxC) implementations of neural networks can be made more resilient against adversarial attacks while virtually retaining their classification accuracy.