Iterated Local Search (ILS) is a metaheuristic that iteratively improves solutions by applying a local search to perturbed solutions. It is designed to be simple, effective, and general-purpose, with a clear separation between problem-specific and general-purpose components. The core idea of ILS is to iteratively build a sequence of solutions using an embedded heuristic, leading to better solutions than random trials. ILS has a long history and has been named variously, including iterated descent, large-step Markov chains, and iterated Lin-Kernighan. The key characteristics of ILS are: (i) a single chain of solutions is followed, excluding population-based algorithms; (ii) the search for better solutions occurs in a reduced space defined by a black-box heuristic. Local search is the most commonly used embedded heuristic, but any optimizer can be used. The purpose of this review is to describe ILS in detail and show its performance. ILS has led to state-of-the-art results with minimal problem-specific knowledge, due to its flexibility and modularity. The chapter is organized into sections discussing the general framework, random restart, searching in S*, perturbation, acceptance criteria, and the optimization of ILS components. Random restart is a simple method to improve solutions found by local search by starting from different points. However, for large instances, it becomes less effective as the distribution of costs becomes more peaked. To overcome this, ILS uses a nested approach, where local search is applied to a reduced space of local optima. This leads to a hierarchy of nested local searches, but the implementation of nearest neighbor search at the level of S* is computationally expensive. Instead, a weaker notion of closeness is used, allowing for faster stochastic search in S*. The ILS procedure involves applying a perturbation to a current solution, then applying local search to the perturbed solution. If the new solution passes an acceptance test, it becomes the next solution in the search. The acceptance criterion determines whether a new solution is accepted, balancing intensification and diversification. The acceptance criterion can be a simple better criterion, a random walk criterion, or a simulated annealing-like criterion that allows for accepting worse solutions with a certain probability. The optimization of ILS involves tuning the initial solution, perturbation, and acceptance criterion. The initial solution can be random or greedy, with greedy solutions often leading to better results. Perturbations can be of fixed or adaptive strength, with adaptive perturbations allowing for better performance. The acceptance criterion can be adjusted to balance intensification and diversification, with simulated annealing-like criteria often providing good results. The local search algorithm is a critical component of ILS, and its performance can significantly affect the overall results. The choice of local search algorithm depends on the problem, with faster but less effective algorithms sometimes being preferable to slower, more powerful ones. The local search algorithm should be optimized to work efficiently with the pertIterated Local Search (ILS) is a metaheuristic that iteratively improves solutions by applying a local search to perturbed solutions. It is designed to be simple, effective, and general-purpose, with a clear separation between problem-specific and general-purpose components. The core idea of ILS is to iteratively build a sequence of solutions using an embedded heuristic, leading to better solutions than random trials. ILS has a long history and has been named variously, including iterated descent, large-step Markov chains, and iterated Lin-Kernighan. The key characteristics of ILS are: (i) a single chain of solutions is followed, excluding population-based algorithms; (ii) the search for better solutions occurs in a reduced space defined by a black-box heuristic. Local search is the most commonly used embedded heuristic, but any optimizer can be used. The purpose of this review is to describe ILS in detail and show its performance. ILS has led to state-of-the-art results with minimal problem-specific knowledge, due to its flexibility and modularity. The chapter is organized into sections discussing the general framework, random restart, searching in S*, perturbation, acceptance criteria, and the optimization of ILS components. Random restart is a simple method to improve solutions found by local search by starting from different points. However, for large instances, it becomes less effective as the distribution of costs becomes more peaked. To overcome this, ILS uses a nested approach, where local search is applied to a reduced space of local optima. This leads to a hierarchy of nested local searches, but the implementation of nearest neighbor search at the level of S* is computationally expensive. Instead, a weaker notion of closeness is used, allowing for faster stochastic search in S*. The ILS procedure involves applying a perturbation to a current solution, then applying local search to the perturbed solution. If the new solution passes an acceptance test, it becomes the next solution in the search. The acceptance criterion determines whether a new solution is accepted, balancing intensification and diversification. The acceptance criterion can be a simple better criterion, a random walk criterion, or a simulated annealing-like criterion that allows for accepting worse solutions with a certain probability. The optimization of ILS involves tuning the initial solution, perturbation, and acceptance criterion. The initial solution can be random or greedy, with greedy solutions often leading to better results. Perturbations can be of fixed or adaptive strength, with adaptive perturbations allowing for better performance. The acceptance criterion can be adjusted to balance intensification and diversification, with simulated annealing-like criteria often providing good results. The local search algorithm is a critical component of ILS, and its performance can significantly affect the overall results. The choice of local search algorithm depends on the problem, with faster but less effective algorithms sometimes being preferable to slower, more powerful ones. The local search algorithm should be optimized to work efficiently with the pert