Quantum technology puts in danger the current cryptographic systems, from the point of view of rendering useless most of the classical algorithms; for example, Shor’s algorithm factors large numbers in polynomial time and Grover’s algorithm speeds up the brute-force search of a key, undermining briefly RSA, ECC and symmetric-key algorithm. In this paper, we first review these historical quantum algorithms and their impact on current cryptosystem deployment, then we discuss PQC schemes with an emphasis on lattice-based primitives as well as the potential roles of QKD for provable security. By performing a thorough investigation of theoretical constructions, practical realizations, and performance trade-offs, we argue that lattice-based and the other PQC schemes exhibits best balance between quantum security, with efficiency, key sizes, integration to 21st century legacy systems tied to their schemes. In the meantime, QKD becomes a complementary approach, providing the unconditional security according with quantum theory, but subjected with the deployment limitations like feasible distance limitation and the hardware ask. Our work puts forward some of the crucial research directions i.e., efficient PQC to real-world applications retargeting algorithm, standard QKD interfaces, and efficient error-correction protocols. By summarizing the known facts related to quantum algorithmic threats and quantum-resistant countermeasures, this work contributes to the roadmap for a truly quantum safe communication society, and provides the design criteria for new security services.