Structured illumination microscopy (SIM) has emerged as an essential technique for three-dimensional (3D) and live-cell super-resolution imaging. However, to date, there has not been a dedicated workshop or journal issue covering the various aspects of SIM, from bespoke hardware and software development and the use of commercial instruments to biological applications. This special issue aims to recap recent developments as well as outline future trends. In addition to SIM, we cover related topics such as complementary super-resolution microscopy techniques, computational imaging, visualization and image processing methods. This article is part of the Theo Murphy meeting issue 'Super-resolution structured illumination microscopy (part 1)'.