These days, devices employing electromagnetic waves, such as antennas, have been intertwined with everyday life such that they are now unrecognizable by a general user. Despite the advancement of these technologies in the past few decades, in recent years, electromagnetic metasurfaces have introduced an unprecedented potential to not only tackle the problems of the conventional systems, but also create new applications for them. These engineered two-dimensional materials offer complete and intimate control over the electromagnetic fields involved through their constituent, judiciously designed meta-atoms. In recent years, in response to emerging applications for these surfaces, there have been tens of proposed meta-atoms that compete in performance, while the search for new applications is ongoing to date. Considering the revolution caused by these structures in different fields, ranging from micro-sized cameras to intelligent buildings, the significance of automated and efficient approaches to design and discover new metasurfaces is undeniable. Inspired by the breakthrough of machine and deep learning methods in other fields, generative machine learning networks such as variational autoencoders and generative adversarial networks are employed to explore the high-dimensional solution space of the meta-atoms composed of metallic and/or dielectric scatterers. Based on the presented generative methods, periodic and quasi-periodic single-layer and multilayer transverse-electric and transverse-magnetic metasurfaces are designed for different applications, including but not limited to frequency selectivity and wideband linear-to-circular polarization conversion. An end-to-end approach involving predicting the dispersive properties of bianisotropic meta-atoms via machine learning surrogate models for a beam-splitting metasurface is also presented. The functionalities of the presented metasurfaces are validated through full-wave simulation tools and experimental measurements. Lastly, future opportunities and design considerations are outlined. While the presented machine learning methods for the design of metasurfaces in this thesis serve as early attempts to tackle the problem, the achieved results demonstrate the capability and versatility of data-driven techniques for different applications of metasurfaces. Due to these remarkable abilities, machine learning will undoubtedly become an indispensable tool for solving increasingly challenging electromagnetic metasurface problems in the near future.