This paper presents Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems. The formulations map these problems to the Ising model, which is a quadratic function of spins, and allow for the use of adiabatic quantum optimization algorithms. The number of spins required is at most cubic in the size of the problem. The paper discusses various NP problems, including partitioning, covering, satisfiability, and others, and provides Ising formulations for each. The formulations are based on the idea that the decision form of the Ising model is NP-complete, and thus can be used to map any NP-complete problem to the Ising model. The paper also discusses the use of gadgets to reduce problems to Ising spin glasses, and the challenges of embedding these problems onto experimental devices. The paper concludes with a discussion of the practical implications of these formulations for quantum computing and the challenges of implementing them on current hardware.This paper presents Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems. The formulations map these problems to the Ising model, which is a quadratic function of spins, and allow for the use of adiabatic quantum optimization algorithms. The number of spins required is at most cubic in the size of the problem. The paper discusses various NP problems, including partitioning, covering, satisfiability, and others, and provides Ising formulations for each. The formulations are based on the idea that the decision form of the Ising model is NP-complete, and thus can be used to map any NP-complete problem to the Ising model. The paper also discusses the use of gadgets to reduce problems to Ising spin glasses, and the challenges of embedding these problems onto experimental devices. The paper concludes with a discussion of the practical implications of these formulations for quantum computing and the challenges of implementing them on current hardware.