Increasing amounts of plastic waste in the environment and their fragmentation into smaller particles known as microplastics (particles, <5 mm) have raised global concerns due to their persistency in the environment and their potential to act as vectors for harmful substances or pathogenic microorganisms. One possible solution to this problem is biodegradation of plastics by microorganisms. However, the scientific information on plastic-degrading microorganisms is scattered across different scientific publications. We conducted a systematic literature review (SLR) with predefined criteria using the online databases of Scopus and Web of Science to find papers on bacterial biodegradation of synthetic petroleum-based polymers. The aims of this SLR were to provide an updated list of all of the currently known bacteria claimed to biodegrade synthetic plastics, to determine and define the best methods to assess biodegradation, to critically evaluate the existing studies, and to propose directions for future research on polymer biodegradation in support of more rapid development of biodegradation technologies. Most of the bacteria identified here from the 145 reviewed papers belong to the phyla Proteobacteria, Firmicutes and Actinobacteria, and most were isolated from contaminated sites, such as landfill sites. Just under a half of the studies (44%) investigated the biodegradability of polyethylenes and derivates, particularly low-density polyethylenes. The methods used to monitor the biodegradation were mainly scanning electron microscopy and Fourier-transform infrared spectroscopy. We propose that: (1) future research should focus on biodegradation of microplastics arising from the most common pollutants (e.g. polyethylenes); (2) bacteria should be isolated from environments that are permanently contaminated with plastics; and (3) a combination of different observational methods should be used to confirm bacterial biodegradation of these plastics. Finally, when reporting, researchers need to follow standard protocols and include all essential information needed for repetition of the experiments by other research groups.