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).