This review covers article and patent data obtained mostly within the period 2013–2023 on the synthesis and biological activity of quinazolines [c]-annelated by five- and six-membered heterocycles. Pyrazolo-, benzimidazo-, triazolo- and pyrimido- [c]quinazoline systems have shown multiple potential activities against numerous targets. We highlight that most research efforts are directed to design of anticancer and antibacterial agents of azolo[c]quinazoline nature. This review emphases both on the medicinal chemistry aspects of pyrrolo[c]-, azolo[c]- and azino[c]quinazolines and comprehensive synthetic strategies of quinazolines annelated at N(3)–C(4) bond in the perspective of drug development and discovery.