Microstrip reflectarray is an antenna which controls its radiation pattern with a number of reflective elements. Conventionally, the reflectarray has been researched to replace curved reflector antennas. In this paper, design theories of reflectarray is briefly introduced, and research trends of high gain and broadband reflectarrays are reviewed. To improve the gain of the reflectarrays, it is required that the reflection phase errors on the reflectarray surface be minimized. For this purpose, sufficiently wide reflection phase range and low phase sensitivity should be realized with the designed element. For bandwidth improvement, the reflection phase of the element should be linear with the frequency variation. In this paper, various researches to improve the reflection phase characteristics of the element for high gain and broadband reflectarrays, such as multi-layer and single-layer multi-resonant structures, are reviewed. Also, dual-reflectarray configuration for compact antenna design is reviewed. Finally, various applications of reflectarrays such as contoured beam, near-field focusing, and RCS reduction are reviewed.