This paper reviews the localized microwave-heating (LMH) phenomenon and its various applications in a paradigmatic approach. A simplified 1-D microwave-heating model is derived for a temperature dependent dielectric medium in a cavity. This semi-analytical model shows the evolution of high-order spatial modes, and the concentration therein of the dissipated power. The LMH effect is associated with the localized hotspot formation due to the thermal-runaway instability. LMH intensification in solids and powders enables various applications using the microwave-drill technique, as reviewed in this paper. These include for instance local heating, up to >10(3)K, also by LDMOS transistors; ignition of thermite powders in air atmosphere and underwater; generation of plasma columns and spheres from molten hotspots in solids (e.g. silicon, titanium), and production of nano-powders by dusty plasma. The potential for 3D-printing and additive manufacturing (AM), recently demonstrated by local solidification of metal powders in a stepwise manner by LMH, is discussed. (C) 2017 Elsevier B.V. All rights reserved.