Optical microscopy is one of the oldest scientific instruments that is still
used in forefront research. Ernst Abbe's nineteenth century formulation of the
resolution limit in microscopy let generations of scientists believe that
optical studies of individual molecules and resolving sub-wavelength structures
were not feasible. The Nobel Prize in 2014 for super-resolution fluorescence
microscopy marks a clear recognition that the old beliefs have to be revisited.
In this article, we present a critical overview of various recent developments
in optical microscopy. In addition to the popular super-resolution fluorescence
methods, we discuss the prospects of various other techniques and imaging
contrasts and consider some of the fundamental and practical challenges that
lie ahead.Comment: 37 pages, 13 figure
