We present recent results related to the modelling, design, and application of graphene surfaces. Mono and multilayer graphene surfaces are patterned in a periodic or quasi-periodic manner to tailor their electromagnetic response in terms of magnitude, phase, or polarization. Applications such as frequency-selective surfaces, polarizers, Faraday rotators, beam-deflectors, and reflectarrays are considered. The structures are analyzed by studying their unit cell response in a period Floquet's environment, using both a commercial and an in-house code, only the latter being able to handle the general graphene dyadic surface conductivity tensor. Due to the significant loss of graphene at microwave frequency, most examples are related to THz frequencies and above.