Air-permeable building envelopes (APBEs) utilize the infiltrated or exfiltrated airflow within porous materials to directly change their temperature distribution to reduce heat loss/gain. APBEs effectively integrate building ventilation and heat recovery to achieve excellent thermal insulation while improving indoor air quality. This paper presents a comprehensive review of the fundamentals and classifications, historical evolution over time, opportunities and benefits, and future views on APBEs. It can be treated as a responsive building envelope that enables building envelopes to dynamically change the U-values by varying the infiltrated or exfiltrated airflow rate within a porous material. Previous studies have indicated that the U-value of 0.1 W/(m2·K) can be realized by employing APBEs. Moreover, some research demonstrates that APBEs could act as high-performance air filters that reduce over 90% of particulate matter within fresh, ventilated air. Some factors, such as airflow rate, thickness, and thermal conductivity of porous materials, have a significant influence on the effectiveness of APBEs. For practical applications, integrating the APBE with passive building ventilation can help reduce the initial cost and facilitate decarbonization in buildings. Moreover, advanced control strategies could collaboratively optimize the operation of ABPEs and build energy systems to maximize their energy-saving potential.