Biomedical entity linking (BioEL) is the process of connecting entities referenced in documents to entries in biomedical databases such as the Unified Medical Language System (UMLS) or Medical Subject Headings (MeSH). The study objective was to comprehensively evaluate nine recent state-of-the-art biomedical entity linking models under a unified framework. We compare these models along axes of (1) accuracy, (2) speed, (3) ease of use, (4) generalization, and (5) adaptability to new ontologies and datasets. We additionally quantify the impact of various preprocessing choices such as abbreviation detection. Systematic evaluation reveals several notable gaps in current methods. In particular, current methods struggle to correctly link genes and proteins and often have difficulty effectively incorporating context into linking decisions. To expedite future development and baseline testing, we release our unified evaluation framework and all included models on GitHub at https://github.com/davidkartchner/biomedical-entity-linking.