Approximate Computing (AxC) is an emerging paradigm that trades algorithmic accuracy for reduced implementation costs, such as lower power consumption or silicon area. While AxC is widely used in error-resilient applications like AI, its application in cryptography has been controversial, as cryptographic schemes are typically intolerant to computational errors. However, Post-Quantum Cryptography (PQC), designed to withstand quantum-enabled attacks, is founded on a new class of cryptographic schemes based on hard learning problems. Notable examples include Learning with Errors (LWE) and its variant, Module-LWE (M-LWE). Since these cryptographic schemes inherently incorporate probabilistic functions and controlled noise generation, it opens new opportunities for AxC-driven hardware optimizations. This talk will explore existing and novel approaches for applying AxC to PQC, leveraging both digital approximate circuits and electrical-level approximations. Finally, it will highlight future research challenges and opportunities at the intersection of AxC and PQC.