Quantum-dot cellular automata (QCA) is a novel promising nanoscale technology that allows the design of integrated circuits with high speed, low power consumption, and high density. Because of this potential benefit, the QCA is chosen as a viable alternative to complementary metal oxide semiconductor (CMOS) technology. In this paper, we have provided a comprehensive review of various types of digital circuits and modules in QCA nanotechnology. We have discussed circuits like XOR/XNOR, half and full adder, multiplexers and demultiplexers, comparators, flip-flops, Arithmetic and Logical Unit (ALU) and Random-Access Memory (RAM). We have shown how these circuits are designed using various methodologies being it using different types of cross-overs, multi-layer designs or using cell-to-cell interaction method advantages and overheads. These logical circuits are compared on the basis of various parameters such as cell area, total area, latency, number of cells, energy dissipation, and complexity and are explained starting from the design which is having large cell count to the efficient design present in terms of the above parameters.