The antenna is one of the key components of satellite communication load. To address the evolving requirements of future satellite communication systems, the sparse planar array has become an important device for transmitting and receiving electromagnetic waves in emerging antenna systems. The advantages of this technology include low cost, low system complexity, and robust anti-interference ability, which have attracted widespread attention within the industry. In this paper, we investigate an optimization design of sparse planar arrays in satellite communication scenarios. Firstly, we introduce the mathematical foundation of the array antennas and establish the optimization design model of the sparse planar array. Secondly, we analyze and compare the impact of different array layout methods on the sparse planar array antenna pattern, and then introduce the latest design trend of array material design. Thirdly, we review some classical optimization methods for optimizing sparse planar arrays and the recent research advancements in promising and novel methods. Lastly, on the basis of the present research status, we propose three future research directions and two critical challenges for optimal design of sparse planar arrays in satellite communication scenarios, which can facilitate the development and realization of array technology under future B5G and 6G wireless networks.