Parkinson’s disease (PD) is known for its motor alterations, but the importance of non-motor symptoms (NMSs), such as olfactory dysfunction (OD), is increasingly recognized. OD may manifest during the prodromal period of the disease, even before motor symptoms appear. Therefore, it is suggested that this symptom could be considered a marker of PD. This article briefly describes PD, the evolution of the knowledge about OD in PD, the prevalence of this NMS and its role in diagnosis and as a marker of PD progression, the assessment of olfaction in patients with PD, the role of α-synuclein and its aggregates in the pathophysiology of PD, and then describes some functional, morphological, and histological alterations observed in different structures related to the olfactory system, such as the olfactory epithelium, olfactory bulb, anterior olfactory nucleus, olfactory tract, piriform cortex, hippocampus, orbitofrontal cortex, and amygdala. In addition, considering the growing evidence that suggests that the cerebellum is also involved in the olfactory system, it has also been included in this work. Comprehending the existing functional and neuroanatomical alterations in PD could be relevant for a better understanding of the mechanisms behind OD in patients with this neurodegenerative disorder.