Sulfonamides constitute an important class of drugs, with many types of pharmacological agents possessing antibacterial, anti-carbonic anhydrase, anti-obesity, diuretic, hypoglycemic, antithyroid, antitumor, and anti-neuropathic pain activities. The sulfonamides have the general formula R-SO2NHR', in which the functional group is bound to an aromatic, heterocycle, aliphatic, and so on. The nature of the R and R' moiety is variable, starting with hydrogen and ranging to a variety of moieties incorporating organic compounds such as coumarin, isoxazole, tetrazole, pyrazole, pyrrole, and so many other pharmaceutical active scaffolds that lead to a considerable range of hybrids named as sulfonamide hybrids. Part A of this review presents the most recent advances in designing and developing two-component sulfonamide hybrids containing coumarin, indole, quinoline, isoquinoline, chalcone, pyrazole/pyrazoline, quinazoline, pyrimidine, thiazole, benzothiazole, and pyridine between 2015 and 2020. Specifically, the authors review the scientific reports on the synthesis and biological activity of this kind of hybrid agent.