COVID-19 (Coronavirus Disease 2019) is an infectious disease caused by SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) and has globally infected 768 million people and caused over 6 million deaths. COVID-19 primarily affects the respiratory system but increasing reports of neurologic symptoms associated with COVID-19 have been reported in the literature. The exact mechanism behind COVID-19 neurologic pathophysiology remains poorly understood due to difficulty quantifying clinical neurologic symptoms in humans and correlating them to findings in human post-mortem samples and animal models. Thus, robust preclinical experimental models for COVID-19 neurologic manifestations are urgently needed. Here, we review recent advances in in vitro, in vivo, and other models and technologies for studying COVID-19 including primary cell cultures, pluripotent stem cell-derived neurons and organoids, rodents, nonhuman primates, 3D bioprinting, artificial intelligence, and multiomics. We specifically focus our discussion on the contribution, recent advancements, and limitations these preclinical models have on furthering our understanding of COVID-19's neuropathic physiology. We also discuss these models' roles in the screening and development of therapeutics, vaccines, antiviral drugs, and herbal medicine, and on future opportunities for COVID-19 neurologic research and clinical management.