Post-Quantum Cryptography (PQC) algorithms should remain secure even in the presence of quantum computers. Although the security of such schemes is guaranteed at the algorithmic level, real-world implementations often suffer from other vulnerabilities like Side-Channel Analysis (SCA) attacks. This Systematization of Knowledge (SoK) paper investigates SCA attacks targeting implementations of PQC algorithms. This work categorizes attacks from an adversarial perspective to identify the most vulnerable components of the algorithms' implementations and highlights unexplored parts in current implementations. In addition, it reviews and analyzes the efficiency and efficacy of existing countermeasures to SCA attacks in current hardware implementations. This approach helps identify countermeasures that provide broader protection and highlights characteristics needed for future secure implementations. Our findings offer guidance in strengthening existing systems and developing more efficient defenses against side-channel attacks.