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The field of high-pressure materials research has grown steadily over the last seven decades, with many remarkable discoveries having been made. This work is part II of a three-part series summarising recent progress in laser material processing within diamond anvil cells (L-DACs); this article focuses on the practice of laser-driven dynamic compression within diamond anvil cells (i.e., LDC–DAC experimentation). In this case, materials are initially pre-compressed within diamond anvil cells, then further dynamically compressed through the use of a high-power pulsed laser, often with the intent to isentropically compress, rather than to heat samples. The LDC–DAC approach provides a novel route to much higher dynamic pressures (approaching 1 TPa), as compared to conventional static compression within a single-stage DAC (<300 GPa) and provides a route to mapping Hugoniot curves. Recent proliferation of low-cost, high-power laser sources has led to increased research activity in LDC–DAC materials processing over the last two decades. Through LDC–DAC experiments, a greater understanding of the properties/structure of cold- and warm-dense matter has been obtained, and novel material phases have been realised. In this article, LDC–DAC experimental methods are reviewed, together with the underlying physics of laser dynamic compression in confined spaces. In addition, a chronology of important events in the development of LDC–DAC processing is provided, and emerging trends, gaps in knowledge, and suggestions for further work are considered.