Along with the increase in life expectancy, a significant increase of people suffering from neurodegenerative diseases (ND) has been noticed. The second most common ND, after Alzheimer’s disease, is Parkinson’s disease (PD), which manifests itself with a number of motor and non-motor symptoms that hinder the patient’s life. Current therapies can only alleviate those symptoms and slow down the progression of the disease, but not effectively cure it. So now, in addition to understanding the mechanism and causes of PD, it is also important to find a powerful way of treatment. It has been proved that in the etiology and course of PD, the essential roles are played by dopamine (DA) (an important neurotransmitter), enzymes regulating its level (e.g., COMT, MAO), and oxidative stress leading to neuroinflammation. Chalcones, due to their “simple” structure and valuable biological properties are considered as promising candidates for treatment of ND, also including PD. Here, we provide a comprehensive review of chalcones and related structures as potential new therapeutics for cure and prevention of PD. For this purpose, three databases (Pubmed, Scopus and Web of Science) were searched to collect articles published during the last 5 years (January 2018–February 2022). Chalcones have been described as promising enzyme inhibitors (MAO B, COMT, AChE), α-synuclein imaging probes, showing anti-neuroinflammatory activity (inhibition of iNOS or activation of Nrf2 signaling), as well as antagonists of adenosine A1 and/or A2A receptors. This review focused on the structure–activity relationships of these compounds to determine how a particular substituent or its position in the chalcone ring(s) (ring A and/or B) affects biological activity.