Micro- and nanoscale structures produced on surfaces of metals, polymers, ceramics, and glasses have many important applications in different fields such as engineering, medical, biological, etc. Laser ablation using ultrashort pulses has become the prominent technique for generating different surface structures for various functional applications. Ultrashort laser ablation proved to be ideal for producing structures with dimensions down to the nanometre scale. In comparison to other texturing techniques employed to create micro/nano features such as electrochemical machining, micro-milling, ion-beam etching, hot embossing, lithography, and mechanical texturing, ultrashort laser ablation produces high-quality surfaces at low cost in a one-step non-contact process. Advantageous characteristics of polymers such as high strength-to-weight ratio, non-corrosive nature, and high electrical and thermal resistance, have made polymers the preferred choice compared to other materials (e.g., steel, aluminium, titanium) in several fields of application. As a result, laser ablation of polymers has been of great interest for many researchers. This paper reviews the current state-of-the art research and recent progress in laser ablation of polymers starting from laser-material interaction, polymer properties influenced by laser, laser texturing methods, and achievable surface functionalities such as adhesion, friction, self-cleaning, and hydrophilicity on commonly used polymeric materials. It also highlights the capabilities and drawbacks of various micro-texturing techniques while identifying texture geometries that can be generated with these techniques. In general, the objective of this work is to present a thorough review on laser ablation and laser surface modification of a variety of industrially used polymers. Since direct laser interference patterning is an emerging area, considerable attention is given to this technique with the aim of forming a basis for follow-up research that could pave the way for potential technological ideas and optimization towards obtaining complex high-resolution features for future novel applications.