Although great progress has been made in the treatment of cancer, the search for new promising molecules with antitumor activity is still one of the greatest challenges in the fight against cancer due to the increasing number of new cases each year. Chalcones (1,3-diphenyl-2-propen-1-one), the precursors of flavonoid synthesis in higher plants, possess a wide spectrum of biological activities including antimicrobial, anti-inflammatory, antioxidant, and anticancer. A plethora of molecular mechanisms of action have been documented, including induction of apoptosis, autophagy, or other types of cell death, cell cycle changes, and modulation of several signaling pathways associated with cell survival or death. In addition, blockade of several steps of angiogenesis and proteasome inhibition has also been documented. This review summarizes the basic molecular mechanisms related to the antiproliferative effects of chalcones, focusing on research articles from the years January 2015–February 2021.