Postoperative tissue flap vitality monitoring enables early detection of clinical complications, allowing for intervention. Timely re-operation can prevent the need for extensive correction procedures, thus reducing healthcare costs and hospitalization time. Statistics show that monitoring can increase the success rate of flap survival to 95% or higher. However, despite the significant progress in monitoring techniques, major and minor complications, leading to the loss of the flap, still occur. This clinical application review aims to provide a comprehensive overview of the recent advancements and findings in flap surgery reconstructions, transplants, and systems for their postoperative assessment. The literature from the years 1925 to 2024 has been reviewed to capture previous and current solutions for monitoring flap vitality. Clinically acclaimed methods and experimental techniques were classified and reviewed from a technical and clinical standpoint. Physical examination, metabolism change, ultrasound method, and electromagnetic (EM) radiation-based measurement methods were carefully evaluated from the perspective of their considered applications. Guidelines aiding engineers in the future design and development process of monitoring systems were proposed. This paper provides a comprehensive overview of the monitoring techniques used in postoperative flap vitality monitoring. It also gives an overview of each approach and potential ways for future development.