Pressure-driven processes have come a long way since they were introduced. These processes, namely Ultra-Filtration (UF), Nano-Filtration (NF), and Reverse-Osmosis (RO), aim to enhance the efficiency of wastewater treatment, thereby aiming at a cleaner production. Membranes may be polymeric, ceramic, metallic, or organo-mineral, and the filtration techniques differ in pore size from dense to porous membrane. The applied pressure varies according to the method used. These are being utilized in many exciting applications in, for example, the food industry, the pharmaceutical industry, and wastewater treatment. This paper attempts to comprehensively review the principle behind the different pressure-driven membrane technologies and their use in the removal of heavy metals from wastewater. The transport mechanism has been elaborated, which helps in the predictive modeling of the membrane system. Fouling of the membrane is perhaps the only barrier to the emergence of membrane technology and its full acceptance. However, with the use of innovative techniques of fabrication, this can be overcome. This review is concluded with perspective recommendations that can be incorporated by researchers worldwide as a new problem statement for their work.