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Spatiotemporal control refers to a class of optical techniques for structuring a laser pulse with coupled spacetime-dependent properties, including moving focal points, dynamic spot sizes, and evolving orbital angular momenta. Here we introduce the concept of arbitrarily structured laser (ASTRL) pulses, which generalizes these techniques. The ASTRL formalism employs a superposition of prescribed pulses to create a desired electromagnetic field structure. Several examples illustrate the versatility of ASTRL pulses to address a broad range of laser-based applications, including laser wakefield acceleration, inertial confinement fusion, nanophotonics, and attosecond physics.