A review of research on the subject of the vaporization and burning of fuel droplets configured in a prescribed array is presented, including both classical works and research over the past decade or two. Droplet arrays and groups and the relation to sprays are discussed. The classical works are reviewed. Recent research on transient burning and vaporization of finite arrays with Stefan convection but without forced convection is presented, including extensions to non-unitary Lewis number and multi-component, liquid fuels. Recent results on transient, convective burning of droplets in arrays are also examined. In particular, transient convective burning of infinite (single-layer periodic and double-layer periodic) and finite droplet arrays are discussed; attention is given to the effects of droplet deceleration due to aerodynamic drag, diameter decrease due to vaporization, internal liquid circulation, and arrays with moving droplets in tandem and staggered configurations. Flame structure is examined as a function of spacing between neighboring droplets and Damkohler number: individual droplet flames versus group flames and wake flames versus envelope flames. Based on existing knowledge of laminar droplet array and spray combustion theory, experimental evidence, and turbulent studies for non-vaporizing and non-reacting two-phase flows, comments are made on the needs and implications for the study of turbulent spray and array combustion. (C) 2014 Elsevier Ltd. All rights reserved.