Laser-heated diamond anvil cell (LH-DAC) experimentation has emerged as a leading technique for materials processing at extreme pressures and temperatures. LH-DAC systems are often employed to better characterise the structure and properties of materials in applications ranging from condensed matter physics to geophysical research to planetary science. This article reviews LH-DAC and related laser-based characterisation, as the first part of a series within the broader context of all high-pressure laser-induced material processing. In part I of this review, a synopsis of laser-heated diamond anvil cell experimental methods, developmental history, fundamental physicochemical processes, and emerging research trends are provided. Important examples of minerals/materials modified during LH-DAC investigations (since their inception) are also tabulated, including key phase transformations, material syntheses, laser parameters, and process conditions—as a reference for the reader and as a guide for directing future research efforts. Note that laser-dynamic-compression within diamond anvil cells (LDC-DAC experimentation) and laser-induced reactive chemical synthesis within diamond anvil cells (LRS-DAC experimentation) are treated separately, as Parts II and III of this review.