memcomputing [1, 2] is a novel physics-based approach to computation that employs time non-locality (memory) to both process and store information on the same physical location. its digital version [3, 4] is designed to solve combinatorial optimization problems. a practical realization of digital memcomputing machines (dmms) can be accomplished via circuits of non-linear dynamical systems with memory engineered so that periodic orbits and chaos can be avoided. a given logic problem is first mapped into this type of dynamical system whose point attractors represent the solutions of the original problem. a dmm then finds the solution via a succession of elementary instantons whose role is to eliminate solitonic configurations of logical inconsistency (``logical defects") from the circuit [5, 6]. i will discuss the physics behind memcomputing and show many examples of its applicability to various combinatorial optimization and machine learning problems demonstrating its advantages over traditional approaches [7, 8]. work supported by darpa, doe, nsf, cmrr, and memcomputing, inc. \\ \\ {[1]} m. di ventra and y.v. pershin, computing: the parallel approach, nature physics 9, 200 (2013). \\ {[2]} f. l. traversa and m. di ventra, universal memcomputing machines, ieee transactions on neural networks and learning systems 26, 2702 (2015). \\ {[3]} m. di ventra and f.l. traversa, memcomputing: leveraging memory and physics to compute efficiently, j. appl. phys. 123, 180901 (2018). \\ {[4]} f. l. traversa and m. di ventra, polynomial-time solution of prime factorization and np-complete problems with digital memcomputing machines, chaos: an interdisciplinary journal of nonlinear science 27, 023107 (2017). \\ {[5]} m. di ventra, f. l. traversa and i.v. ovchinnikov, topological field theory and computing with instantons, annalen der physik 529,1700123 (2017). \\ {[6]} m. di ventra and i.v. ovchinnikov, digital memcomputing: from logic to dynamics to topology, annals of physics 409, 167935 (2019). \\ {[7]} f. l. traversa, p. cicotti, f. sheldon, and m. di ventra, evidence of an exponential speed-up in the solution of hard optimization problems, complexity 2018, 7982851 (2018). \\ {[8]} f. sheldon, f.l. traversa, and m. di ventra, taming a non-convex landscape with dynamical long-range order: memcomputing ising benchmarks, phys. rev. e 100, 053311 (2019).