Scanning probe microscopy (SPM), a key invention in nanoscience, has by now been extended to a wide spectrum of basic and applied fields. Its application to basic science led to a paradigm shift in the understanding and perception of matter at its nanoscopic and even atomic levels. SPM uses a sharp tip to physically raster-scan samples and locally collect information from the surface. Various signals can be directly detected by SPM in real space with atomic or nanoscale resolution, which provides insights into the structural, electronic, vibrational, optical, magnetic, (bio)chemical and mechanical properties. This Primer introduces the key aspects and general features of SPM and SPM set-up and variations, with particular focus on scanning tunnelling microscopy and atomic force microscopy. We outline how to conduct SPM experiments, as well as data analysis of SPM imaging, spectroscopy and manipulation. Recent applications of SPM to physics, chemistry, materials science and biology are then highlighted, with representative examples. We outline issues with reproducibility, and standards on open data are discussed. This Primer also raises awareness of the ongoing challenges and possible ways to overcome these difficulties, followed by an outlook of future possible directions.