This chapter discusses the evolution of wave-material interaction using engineered surfaces and its application in antenna engineering. The discussions include design of high-gain antennas, multi-beam antennas, and antennas with OAM radiation. Metasurfaces which are two-dimensional (2D) equivalents of metamaterials that can invoke electromagnetic phenomena beyond natural limit are one of the solutions to address the difficulty in complex metamedia. This discussion starts with fundamental physics of metasurface followed by a short review on bottlenecks in transformation electromagnetic-based metamaterial devices. The chapter also includes fundamental of subwavelength elements types, followed by investigations on the basic subwavelength elements (meta-elements) like patch, ring, cross, slot, and Jerusalem. These meta-elements are studied for phase tuning. Further investigations showed that a remodeled Jerusalem cross-type meta-element could produce approximate 360° phase swing. Another aspect of the research is compact antennas with improved radiation characteristics. The discussion includes the design of a high-gain planar antenna fed reflector by quantizing the reflection phase of remodeled Jerusalem meta-element. The chapter also describes realization of a quad-beam reflector fed by an microstrip antenna using alternating projecting method (APM). Measured results of all experiments have a good agreement with the simulated results. Based on phase quantization, experimental realization of two types of vortex generating antennas using phased surfaces was also possible. A CAD simulated study on the behavior of these antennas on electrically large platforms was made.