Rayleigh's criterion is extensively used in optical microscopy to determine the resolution of microscopes. Despite its widespread use, it is well known that this criterion is based on heuristic notions and can be surpassed in a regular optical microscope. The inadequacy of Rayleigh's criterion has necessitated a reassessment of the resolution limits of optical microscopes. The thesis proposes a new resolution criterion that overcomes the limitations of Rayleigh's criterion. The new result predicts that there is no resolution limit, but that the resolvability depends on the number of detected photons. Analytical tools are introduced to estimate the distance from microscopy images. By imaging fluorescently labeled DNA nano-rulers, it is shown that distances as small as 12 nm can be measured from experimental data with accuracy as predicted by the new resolution criterion. The new result is derived by adopting a stochastic framework and using the theory concerning the Fisher information matrix. This approach is generalized to a wide variety of estimation problems in optical microscopy by deriving expressions for the limits to the accuracy of the parameter estimates. As an application, the thesis addresses the location estimation problem. Analytical formulae are derived that provide a limit to the accuracy with which the location of a microscopic object can be determined. These results are illustrated by considering specific image profiles that describe the image of a single molecule. Another contribution of this thesis is the development of a new microscopy technique called multifocal plane microscopy for tracking single molecules/particles in 3D. An important property of this technique is its improved depth discrimination capability, which in turn enables accurate determination of the axial location of the particle especially when it is close to the plane of focus.