Laser ablation (LA), which employs a pulsed laser to remove materials from a substrate for generating micro-/nanostructures, has tremendous applications in the fabrication of metals, ceramics, glasses and polymers. It has become a noteworthy approach for achieving various functional structures in engineering, chemistry, biology, medicine and other fields. Polymers are one such class of materials; they can be melted and vaporized at high temperature during the ablation process. A number of polymers have been researched as candidate substrates in LA, and many different structures and patterns have been realized by this method. The current states of research and progress are reviewed from basic concepts to optimal parameters, polymer types and applications. The significance of this paper is to provide a basis for follow-up research that leads to the development of superior materials and high-quality production through LA. In this review, we first introduce the basic concept of LA, including mechanism, laser types (millisecond, microsecond, nanosecond, picosecond and femtosecond) and influential parameters (wavelength, repetition rate, fluence and pulse duration). Then, we focus on several commonly used polymer materials and compare them in detail, including the effects of polymer properties, laser parameters and feature designs. Finally, we summarize the applications of various structures fabricated by LA in a variety of areas along with a perspective of the challenges in this research area. Overall, a thorough review of LA of several polymers is presented, which could pave the way for characterization of future novel materials.