Thiosemicarbazones (TSC) are a subclass of iron-chelating agents that are believed to have an anticancer activity. The high potential for the application of this compound class can be illustrated by a fact that three TSC have entered clinical trials. The ability to chelate metal ions results in several biochemical changes in the cellular metabolism and growth. An important factor that determines the antitumor activity of TSC is a level of iron regulatory proteins and the antioxidant potential that is specific for each type of cancer cell. However, despite the increasing interest in TSC, their mechanism of anticancer activity is still unclear. For a more effective and rational design, it is crucial to determine and describe the abovementioned issues. In this report, we describe a series of new TSC that are designed on the four main structural scaffolds. The anticancer activity of these compounds was evaluated against a panel of cancer cell lines including colon and breast cancers and gliomas. Special attention was paid to the metal-dependent proteins. The impact of the tested TSC on the cell cycle and redox homeostasis was also determined. These results confirm a p53-independent mechanism of apoptosis.