Recent and upcoming space applications demand advanced high-gain antennas onboard the satellites to meet challenging specifications in terms of bandwidth or multibeam operation. Reflectarray antennas are emerging as a potential candidate for these applications due to their planar and lightweight reflecting surface, easily integrated with the satellite platform. In the recent SWOT, MARCO, and ISARA missions from NASA, reflectarrays have been integrated into the spacecraft by dividing the surface into multiple flat panels and deploying them as a single-facet aperture. However, this approach limits the bandwidth of the antenna due to the differential spatial phase delay effect. The use of conformal apertures approaching a curved profile can mitigate this effect, providing broader bandwidths and improved antenna performances. This chapter is dedicated to the comprehensive analysis and design of different non-planar aperture antennas based on reflectarrays, including multifaceted and doubly curved surfaces, engineered to exhibit electrical and mechanical performance suitable for space applications.