Hybrid methods for the design and analysis of reflectarrays and non-timed arrays are proposed. These hybrid methods seek to address fundamental challenges facing the use of reflectarrays or phased arrays in satellite communications given recent industry trends. Specifically, this dissertation addresses: 1) reflectarray unit-cell design for wideband and circular polarization, 2) a method of far field computation given power handling and sidelobe accuracy considerations, 3) modeling and mitigation of time-delay error for non-timed arrays, and 4) preliminary research on a machine learning-based antenna pointing and tracking algorithm. Each hybrid method is presented in a theoretical framework with algorithmic implementation details and simulation results; these results are validated using rigorous solution techniques or commercial full-wave solvers to prove, by comparison, the hybrid methods accuracy and viability. All of these results are based on original, peer-reviewed, and published research by the author. The findings of this work suggest that by employing the proposed hybrid methods therein, an adaptive reflectarray or non-timed array can be fully designed and characterized for high performance satellite communications in ways that were before not possible.