With the emergence of fifth-generation (5G) cellular networks, millimeter-wave (mmW) and terahertz (THz) frequencies have attracted ever-growing interest for advanced wireless applications. The traditional printed circuit board materials have become uncompetitive at such high frequencies due to their high dielectric loss and large water absorption rates. As a promising high-frequency alternative, liquid crystal polymers (LCPs) have been widely investigated for use in circuit devices, chip integration, and module packaging over the last decade due to their low loss tangent up to 1.8 THz and good hermeticity. The previous review articles have summarized the chemical properties of LCP films, flexible LCP antennas, and LCP-based antenna-in-package and system-in-package technologies for 5G applications, although these articles did not discuss synthetic LCP technologies. In addition to wireless applications, the attractive mechanical, chemical, and thermal properties of LCP films enable interesting applications in micro-electro-mechanical systems (MEMS), biomedical electronics, and microfluidics, which have not been summarized to date. Here, a comprehensive review of flexible LCP technologies covering electric circuits, antennas, integration and packaging technologies, front-end modules, MEMS, biomedical devices, and microfluidics from microwave to THz frequencies is presented for the first time, which gives a broad introduction for those outside or just entering the field and provides perspective and breadth for those who are well established in the field.