Synthetic jets (SJs) are becoming increasingly popular in aerospace engineering due to their potential applications in flow mixing enhancement, boundary layer control, and thermal load reduction. These pulsating jets involve the periodic motion of fluid in and out of a cavity through an orifice generated by a vibrating diaphragm at the cavity base. SJs are unique because they comprise working fluid and do not require an external fluid source, setting them apart from conventional flow control techniques. Although the net mass flux is zero in a complete cycle, there is a finite net momentum flux due to the imbalanced flow conditions across the orifice, and hence SJs are also known as Zero Net Mass Flux (ZNMF) jets. Numerous experimental and numerical studies have evaluated the efficacy of SJs in controlling the flow and heat transfer characteristics under various conditions, including quiescent and cross-flow situations. This review provides a comprehensive overview of the progress in synthetic jet applications in the last 40 years, specifically focusing on their potential use in flow control, heat transfer, and related applications in aerospace engineering. The strengths and limitations of SJs are discussed, and critical areas are identified for future research and development, including further optimization and refinement of these unique jets.