Advances in metalens technology have had an important impact on the development of optics. Different from traditional lenses, metalens materials are not limited to the intrinsic permittivity and permeability of natural materials. Metalenses are composed of artificially designed sub-wavelength cell structures, and the optical wavefront is manipulated through phase mutations, breaking through the limitations of the shape and thickness of the lens surface and achieving super-resolution imaging. Due to its advantages of lightness thinness, compactness and high integration, metalenses improve the excessive volume and mass of traditional lenses, meet the miniaturization needs of modern complex optical systems, and meet the needs of current portable devices for fast and stable imaging. Large field of view metalenses, achromatic metalenses and zoom metalenses are the representative elements of metalens imaging, which have great advantages in the design of optical systems. Large field of view metalenses have a larger field of view and can be integrated with image sensors, improving the detection range of small devices such as lidar and planar cameras. Achromatic metalenses have a wider working bandwidth, which solves the problem that traditional light field cameras cannot broadband achromatic, and has broad application prospects in the fields of robot vision and vehicle sensing, and is of great significance for multispectral analysis and optical communication. The zoom lens has flexible focal length variation, improves the large size and weight of traditional zoom lenses, and solves the problem of liquid zoom lenses being susceptible to interference, providing fast response times in vision systems for biological microscopy, multi-depth imaging, and autonomous vehicles. The design methods of existing large field of view metalenses, achromatic metalenses, and zoom metalenses are summarized, their existing problems are analyzed, and the challenges faced by metalenses are studied, including the trade-offs between chromatic aberration correction and field of view, the improvement of numerical aperture, and the improvement of zoom stability and efficiency, and predict the development trend of metalenses. The insights and advances presented in this study are expected to inspire further exploration and application of metalenses, paving the way for next-generation optical technologies. Different phase control principles of metal lenses, the corresponding metal lenses, their advantages and applications are introduced. The design methods of three metal lenses with different functions are reviewed, the principles and application scope of these metal lenses are summarized, and the shortcomings and future development trends of metal lenses are analyzed. The three types of metalenses are: 1) Large field of view metalenses, including those that rotate bilayer metasurfaces to achieve large field of view focusing, and metalens arrays integrated with CMOS. 2) Achromatic metalenses, including metalenses with separate wavelength focusing, metalenses with simultaneous control of transmission phase and geometric phase, and metalenses with complementary unit structures and shapes. 3) Zoom metalenses, including those that zoom by adjusting the crystalline state of the unit cell structure material, and those that are focused by wavelength changes. Combined with the actual needs of metalenses, the above different functions can be combined and designed, such as the secondary phase metalens that realizes the function of large field of view and achromatic at the same time, and the metalens that adjusts the focal length through mechanical steps to achieve the function of large field of view and zoom. Throughout the discussion, we emphasized the importance of focusing on performance parameters such as efficiency, NA, FOV, etc., which are the benchmarks for evaluating the effectiveness of metalenses in real-world applications. Finally, we discussed the challenges faced by the development of metalenses, which have certain guiding significance for the future development of metalenses. The major progress made in the basic principles, unit structures and lens materials of metal lenses is summarized, and the development history and technical route of large field of view, achromatic and zoom metal lenses are presented. This article analyzes these metalens focusing techniques and discusses key performance indicators such as working bandwidth, focusing efficiency, NA, field of view, zoom range, etc. At the same time, the application scenarios and challenges of existing metalenses with large field of view, achromatic and zoom are also analyzed. Finally, some suggestions are put forward for the future development of metalenses, including how to balance the large field of view and working bandwidth, how to balance the achromatic function and high NA, and how to achieve high-speed and stable zoom. In summary, the design research of metalenses will promote the development of the next generation of high-performance, high-efficiency, and high-integration optical systems and display systems.