For decades, photovoltaic-thermal hybrid solar systems (PVT) have been presented in a single unit to combine PV cells and solar thermal absorbers to increase solar utilization and reduce the relative cost per unit installation area. The building-integrated photovoltaic-thermal configuration (BIPV/T) has exploited the envelope or roof of buildings with PVT assemblies to produce both heat and electricity. Consequently, the BIPV/T system provides a viable way for reducing energy consumption and achieving low-energy building requirements. This study provides an up-to-date review of the current developments in the individual and combined BIPV/T systems. It focuses on the multiple numerical and experimental investigations undertaken to evaluate the design and performance of the various wall- and roof-mounted BIPV/T configurations, such as the BIPV/T air-cooled systems, BIPV/T water-cooled systems, BIPV/T systems with concentrators, and PCM-based BIPV/T systems. The effects of several explored parameters on the building performance, energy, exergy, energy savings, etc. have been analyzed. The systems designs, their benefits and drawbacks, performance indicators, developments, and limitations have been analyzed. The literature research revealed that BIPV/T air systems could achieve optimal performance if the ideally designed characteristics, such as tilt angles, configuration arrangements, and fluid flow rate, were chosen correctly. On contrary, the BIPV/T water-cooled systems have demonstrated better thermal performance, but with additional manufacturing costs. Additionally, with the integration of the BIPV/T systems with other systems, such as HVAC and heat recovery systems, the benefits to utilization and techno-economic performance were maximized. Under the same testing settings, hybrid BIPV/T-PCM and BIPV/T with concentrators have produced superior results compared to air- and water-cooled BIPV/T systems. The review provides several conclusions and highlights challenges with recommendations for future research topics that should be followed to sustain the use of BIPV/T systems.