MAX phases – Past, present, and future

[Display omitted] •Number of experimentally reported MAX phases has doubled since 2019 to more than 342.•Elemental combinations expanded via alloying, high-entropy and top-down synthesis routes.•Article introduces a MAX phase classification based on how they are synthesized.•New MAX phases for future synthesis are identified by phase stability predictions. The MAX phases are a class of nanolaminated materials composed of an early transition-metal (M), an A-group element (A) and C, N, B and/or P (X). Progress in MAX phase research in recent years has increased their number from the original 50 or so, to more than 300 phases. Since half of the 342 MAX phases have been discovered after 2018, an overview of the progress made in the field is timely. Currently, 28 M elements, 28 A elements, and 6 X elements have been incorporated in the MAX phases, alloys included. We further categorize MAX phases based on the synthesis route used to make them; if made via a one-step approach in bottom-up synthesis or formed through elemental replacement reactions in top-down synthesis. This classification is also correlated to theoretical phase stability predictions, that in turn, can be used to identify novel synthesizable MAX phase compositions as well as to suggest suitable synthesis routes. Furthermore, using phase stability predictions we identify 182 new theoretically stable MAX phases awaiting experimental confirmation. Notably, as MAX phases are precursors for MXenes, the dramatically increased interest in the latter for a large host of potential applications renders the former even more valuable.