Membrane technology is playing a crucial role in cutting-edge innovations in the biomedical field. One such innovation is the surface engineering of a membrane for enhanced longevity, efficient separation, and better throughput. Hence, surface engineering is widely used while developing membranes for its use in bioartificial organ development, separation processes, extracorporeal devices, etc. Chemical-based surface modifications are usually performed by functional group/biomolecule grafting, surface moiety modification, and altercation of hydrophilic and hydrophobic properties. Further, creation of micro/nanogrooves, pillars, channel networks, and other topologies is achieved to modify physio-mechanical processes. These surface modifications facilitate improved cellular attachment, directional migration, and communication among the neighboring cells and enhanced diffusional transport of nutrients, gases, and waste across the membrane. These modifications, apart from improving functional efficiency, also help in overcoming fouling issues, biofilm formation, and infection incidences. Multiple strategies are adopted, like lysozyme enzymatic action, topographical modifications, nanomaterial coating, and antibiotic/antibacterial agent doping in the membrane to counter the challenges of biofilm formation, fouling challenges, and microbial invasion. Therefore, in the current review, we have comprehensibly discussed different types of membranes, their fabrication and surface modifications, antifouling/ antibacterial strategies, and their applications in bioengineering. Thus, this review would benefit bioengineers and membrane scientists who aim to improve membranes for applications in tissue engineering, bioseparation, extra corporeal membrane devices, wound healing, and others.