Nanogels and microgels are soft, deformable and penetrable objects with an internal gel-like structure that is swollen by the dispersing solvent. Their softness and the potential to respond to external stimuli like temperature, pressure, pH, ionic strength and different analytes make them interesting as soft model systems in fundamental research as well as for a broad range of applications, in particular in the field of biological applications. Recent tremendous developments in their synthesis open access to systems with complex architectures and compositions allowing for tailoring microgels with specific properties. At the same time state-of-the-art theoretical and simulation approaches offer deeper understanding of the behavior and structure of nano- and microgels under external influences and confinement at interfaces or at high volume fractions. Developments in the experimental analysis of nano- and microgels have become particularly important for structural investigations covering a broad range of length scales relevant to the internal structure, the overall size and shape and inter-particle interactions in concentrated samples. Here we provide an overview of the state-of-the-art, recent developments as well as emerging trends in the field of nano- and microgels. The following aspects build the focus of our discussion: Tailoring (multi-)functionality through synthesis; the role in biological and biomedical applications; the structure and properties as model system, e.g. for densely packed arrangements in bulk and at interfaces; as well as the theory and computer simulation.