Recently, there has been growing interest in the use of metamaterial (MTM)-based lenses, also known as metalenses, as innovative antenna technology. Increasingly widespread applications of metalenses in modern microwave communication and sensing systems have been found, following the development of the first microwave artificial lens in the 1940s based on the concept of an artificial dielectric, which was later broadly termed an "MTM." This article examines the evolution of metalens antennas over the past 80 years and introduces the principles and technologies underlying their design. It then focuses on the latest progress in the research on and applications of MTMs and metasurface (MTS)-based metalens antennas. The principles and basic structures of transmissive focusing metalens antennas in the microwave band are elaborated. Selected metalens antennas are introduced chronologically, starting with metallic waveguide lens antennas, followed by metallic or metal-dielectric Fresnel zone plate lens antennas, transmitarray lens antennas, MTS lens antennas, and flat transformation-optics-based MTM Luneburg lens antennas. The technical merits, challenges, applications, trends, and future research of each type of metalens antenna are also addressed. The information presented in this article will benefit the research, development, and application of metalens antennas in fifth-and beyond-generation communications, Wi-Fi 6 short-range connections, and next-generation microwave sensing and imaging systems.