Metasurfaces constitute a class of thin metamaterials, which are used to control plane waves and surface waves, i.e. to enable new radiation and guiding properties. Metasurfaces can be employed for realizing highly customizable EM devices from microwave to optical frequencies. During this course the background and theory of different types of metasurfaces will be explained, as well as how to implement these theoretical models in different numerical methods and practical designs. The work will be presented in relation to specific applications such as: controllable “smart” surfaces, new types of antennas, flat optics, devices for tailoring wavefronts, novel wave-guiding structures, directivity enhancement, reduction of far out sidelobes and tunable active metasurface structures.