What is superresolution microscopy?

I explain what is, what is not, and what is only sort of superresolution microscopy. I discuss optical resolution, first in terms of diffraction theory, then in terms of linear systems theory, and finally in terms of techniques that use prior information, nonlinearity, and other tricks to improve performance. The discussion reveals two classes of superresolution: Pseudo superresolution techniques improve images up to the diffraction limit but not much beyond. True superresolution techniques allow substantial, useful improvements beyond the diffraction limit. The two classes are distinguished by their scaling of resolution with photon counts. Understanding the limits to imaging resolution involves concepts that pertain to almost any measurement problem, implying that the framework given here has broad application beyond optics.