A polymerase chain reaction (PCR) is a method typically active in genetic research, especially to amplify or copy genes. Herein, the application of microfluidic devices for nucleic acid amplification has recently been extensively and vigorously studied and implemented. However, the existing classical instruments are hefty, excessive thermal loss, more power consumption, laborious, and require more execution time. Further, it is hard to establish a platform to integrate, automate, and miniaturize the microdevice on a solo stage for testing and analyzing. There has been substantial innovation in the development of continuous-flow based microfluidic PCR micro-devices in the last few decades because of their widespread applications. The continuous-flow microfluidic PCR microdevice enables several features like compact device, portability, repeatability, miniaturization, and integration with a marginal sample reaction volume. It also permits rapid testing and identification of the genetic sample with high-throughput and increased efficiency and output stability of the microdevice by using minimum accessories for its operation. In this review, the recent trends towards the advancement and miniaturization of the assessments using PCR technique with many distinct novel based microchannel designs, fabrication and bonding method, and other associated approaches in the development of continuous-flow based microfluidic PCR devices for the quantification and detection of the nucleic acids. This review discusses concepts like Automation, Integration, and Miniaturization (AIM) with different approaches and applications using continuous-flow based PCR devices.