The literature on drying sessile droplets and deposition of suspended material is reviewed including the simple explanation of the "coffee ring" deposit given by Deegan et al.(1) Analytical and numerical solutions for the flow are given, including the effect of Marangoni stresses, pinning or movement of the contact line, and viscous, thermal, gravitational, and other effects. The solution space is explored using dimensionless groups governing mass, momentum, and heat transfer effects in the droplet, external gas, and substrate. The most common types of deposition patterns are summarized, including those produced by pinned contact lines, sticking-and-slipping contact lines, and Marangoni effects. The influence of contact-line deposits is also reviewed, and the effects of colloidal, polymeric, and other depositing materials. Advanced applications from ink-jet printing to disease diagnosis are discussed as well. The review helps readers take stock of what has been learned and what remains incompletely explained. (c) 2014 American Institute of Chemical Engineers AIChE J, 60: 1538-1571, 2014