Olfactory dysfunction (OD) is one of the most common symptoms in COVID-19 patients and can impact patients' lives significantly. The aim of this review was to investigate the multifaceted impact of COVID-19 on the olfactory system and to provide an overview of magnetic resonance (MRI) findings and neurocognitive disorders in patients with COVID-19-related OD. Extensive searches were conducted across PubMed, Scopus, and Google Scholar until 5 December 2023. The included articles were 12 observational studies and 1 case report that assess structural changes in olfactory structures, highlighted through MRI, and 10 studies correlating the loss of smell with neurocognitive disorders or mood disorders in COVID-19 patients. MRI findings consistently indicate volumetric abnormalities, altered signal intensity of olfactory bulbs (OBs), and anomalies in the olfactory cortex among COVID-19 patients with persistent OD. The correlation between OD and neurocognitive deficits reveals associations with cognitive impairment, memory deficits, and persistent depressive symptoms. Treatment approaches, including olfactory training and pharmacological interventions, are discussed, emphasizing the need for sustained therapeutic interventions. This review points out several limitations in the current literature while exploring the intricate effects of COVID-19 on OD and its connection to cognitive deficits and mood disorders. The lack of objective olfactory measurements in some studies and potential validity issues in self-reports emphasize the need for cautious interpretation. Our research highlights the critical need for extensive studies with larger samples, proper controls, and objective measurements to deepen our understanding of COVID-19's long-term effects on neurological and olfactory dysfunctions.