Printed reflectarrays are low-cost, low-profile high gain antennas demonstrating distinctive advantages over conventional parabolic reflectors and phased-arrays. The flat, low weight reflecting surface of a reflectarray makes it an attractive alternative with respect to bulky parabolic reflectors specially for space and satellite systems. As compared to high-cost phased-array antennas, with incorporation of solid state devices, reflectarrays are able to demonstrate electronic beam scanning in a very low-cost way. A distinctive advantage of a reflectarray antenna lies in its potential to be readily designed as a multi-band antenna which demonstrates independent performance at several frequencies. A characteristic that is difficult to achieve using conventional parabolic reflectors. The aim of this thesis is to present low-cost, simple, multi-band printed reflectarray antennas in Ku and THz frequency bands. In Ku band we present a dual-band reflectarray performing at 12 and 14 GHz and a quad-band reflectarray antenna performing at 12, 13, 14 and 15.5 GHz. The presented prototypes benefit from the advantage of having a single-layer structure which reduces the design complexity as well as the fabrication cost. In addition, multi-band reflectarrays are able to perform at any polarization due to the dual-linear polarized design of their unit-cells. Furthermore, the design of the unit-cell is such that, at each frequency, the phase response depends on only one parameter of the cell. This advantage eliminates the need for time consuming optimizations. Based on proposed unit-cells dual-band and quad-band reflectarrays with arbitrary beam direction versus frequency have been simulated, fabricated and measured. Simulation and measurement results as well demonstrate the satisfactory independent performance of the prototypes at each intended frequency. In THz region, for the first time we present a tri-band unit-cell based on which reflectarray prototypes performing at the three frequencies 0.7, 1.0 and 1.5 THz, are designed. The presented reflectarrays possess all the advantages of those designed for Ku band with the additional advantage of having high resistivity silicon as the substrate thanks to a sophisticated fabrication process. The use of silicon as substrate is a big advantage since it facilitates the integration of solid state devices for reconfigurability. Based on the proposed unit-cell reflectarray samples with arbitrary independent performance at each frequency are designed, simulated, fabricated and measured. Measurement results obtained using a THz-TDS (Terahertz Time-Domain Spectroscopy) measurement system, demonstrate the satisfactory independent performance of the reflectarray samples at each frequency. This thesis also presents a dual-band, dual-polarized reconfigurable unit-cell for beam-scanning reflectarray operating at 12 and 14 GHz. The cell however suffers from high-cross-polarization level. A chessboard cell arrangement is proposed to mitigate the high cross-polarization level at the reflectarray far-field region. Simulation results show the effectiveness of the chessboard arrangement in eliminating the cross-polarization allowing the design of a low-cross polarization reconfigurable reflectarray antenna out of a unit-cell with high cross-polarization level. Finally, the thesis presents the concept of a versatile flat prism which is a reflectarray with a pre-designed frequency-scanning behaviour. The limitations and challenges as well as solutions for implementation of such a device are presented and discussed.