Polymer gels are widely used in oil–gas drilling and production engineering for the purposes of conformance control, water shutoff, fracturing, lost circulation control, etc. Here, the progress in research on three kinds of polymer gels, including the in situ crosslinked polymer gel, the pre-crosslinked polymer gel and the physically crosslinked polymer gel, are systematically reviewed in terms of the gel compositions, crosslinking principles and properties. Moreover, the advantages and disadvantages of the three kinds of polymer gels are also comparatively discussed. The types, characteristics and action mechanisms of the polymer gels used in oil-gas drilling and production engineering are systematically analyzed. Depending on the crosslinking mechanism, in situ crosslinked polymer gels can be divided into free-radical-based monomer crosslinked gels, ionic-bond-based metal cross-linked gels and covalent-bond-based organic crosslinked gels. Surface crosslinked polymer gels are divided into two types based on their size and gel particle preparation method, including pre-crosslinked gel particles and polymer gel microspheres. Physically crosslinked polymer gels are mainly divided into hydrogen-bonded gels, hydrophobic association gels and electrostatic interaction gels depending on the application conditions of the oil–gas drilling and production engineering processes. In the field of oil–gas drilling engineering, the polymer gels are mainly used as drilling fluids, plugging agents and lost circulation materials, and polymer gels are an important material that are utilized for profile control, water shutoff, chemical flooding and fracturing. Finally, the research potential of polymer gels in oil–gas drilling and production engineering is proposed. The temperature resistance, salinity resistance, gelation strength and environmental friendliness of polymer gels should be further improved in order to meet the future technical requirements of oil–gas drilling and production.