The use of organic fluorescent probes in biochemical and biophysical applications of single molecule spectroscopy and fluorescence microscopy techniques continues to increase. As single molecule measurements become more quantitative and new developments in super-resolution imaging allow researchers to image biological materials with unprecedented resolution, it is becoming increasingly important to understand how the properties of the probes influence the signals measured in these experiments. In this review, we focus on the photochemical and photophysical processes of organic fluorophores that affect the properties of fluorescence emission. This includes photobleaching, quenching, and the formation of non-emissive (dark) states that result in fluorescence blinking in a variety of timescales. These processes, if overlooked, can result in an erroneous interpretation of the data. Understanding their physical origins, on the other hand, allows researchers to design experiments and interpret results so that the maximum amount of information about the system of interest can be extracted from fluorescence signals.