Over the past decade, three-dimensional fluorescence microscopy has become an integral part of investigations into cell structure, function and dynamics.   While light microscopy can provide nearly ideal sensitivity and selectivity, and the unique ability to examine the 3D interior of living samples, its resolution is fundamentally limited by physical law due to the rather coarse wavelength of visible light.   We are developing approaches to extend resolution, and to eliminate effects of aberrations that plague three-dimensional light microscopy.   Here we report on new classes of widefield microscopes invented by Mats Gustafsson that extend resolution well beyond the classical limits.   Based on information theory, we have shown that spatially structured illumination makes it possible to double both the lateral and axial resolution, to around 100 and 300nm respectively.   With an independent concept, the axial resolution can be improved sevenfold beyond that of conventional microscopes, to about 90nm, using two opposing objective lenses to create interference in both the excitation and the emission light.   These methods can be combined to provide nearly isotropic 100nm resolution.   Very recent results, exploiting nonlinear effects, demonstrate that there is in fact no theoretical limit to how far the resolution can be increased, with the ultimate limits being dictated by practical concerns of signal-to-noise and not by physical law.   To date, we have reached a 2D resolution better than 60nm, to our knowledge the highest XY resolution ever achieved with far-field visible light.