Metasurfaces are nanopatterned structures of sub-wavelength thickness. Their effective refractive index and spectral characteristic can be tailored by material composition, intrinsic and extrinsic resonances, structure size, and ambient conditions. Consequently, they allow for phase, amplitude, polarisation, and spatial control of an optical field beyond what natural materials can offer. Dielectric metasurfaces with lower loss have opened a wide range of new applications such as enhanced imaging, structural colour, holography, and planar sensors. In particular, beam steering and control measures such as nonlinear optics, ultrafast optics, and quantum optics are of increasing importance for quantum communication, computation, and information processing. In this review, the recent progress on dielectric metasurfaces is summarised, including advanced fabrication technologies and novel applications from advanced wavefront shaping to quantum platforms. In addition, a perspective for the future development of the field is presented.