Widefield fluorescence microscopy is seeing dramatic improvements in resolution, reaching today 100 nm in all three dimensions. This gain in resolution is achieved by dispensing with uniform Köhler illumination. Instead, non-uniform excitation light patterns with sinusoidal intensity variations in one, two, or three dimensions are applied combined with powerful image reconstruction techniques. Taking advantage of non-linear fluorophore response to the excitation field, the resolution can be further improved down to several 10 nm. In this review article, we describe the image formation in the microscope and computational reconstruction of the high-resolution dataset when exciting the specimen with a harmonic light pattern conveniently generated by interfering laser beams forming standing waves. We will also discuss extensions to total internal reflection microscopy, non-linear microscopy, and three-dimensional imaging.