This paper presents an overview of efficient algorithms for the nearest neighbor problem, both approximate and exact. The goal is to preprocess a set of objects (e.g., images) so that, given a new query object, the algorithm can quickly return the closest object in the set. This problem is of great interest in various fields, including data compression, databases and data mining, information retrieval, image and video databases, machine learning, pattern recognition, and statistics. The paper is divided into two main parts. First, it provides an overview of a series of algorithms for the nearest neighbor problem based on the concept of locality-sensitive hashing (LSH). These algorithms have already found practical applications. Second, it describes recently discovered hash-based algorithms for d-dimensional Euclidean space. These algorithms are believed to be nearly optimal. The paper begins by defining the nearest neighbor problem. Given a set of n points, the goal is to build a data structure that, for any query point, returns the closest point in the set. This problem is particularly interesting when the points are in a d-dimensional space with a distance function, such as Euclidean distance. The features of objects (e.g., images) are often represented as points in R^d, and the distance metric is used to measure similarity between objects. The basic problem is then to index these features and perform similarity searches. When the dimension d is small (up to 10 or 20), efficient algorithms exist. One such data structure is the kd-tree, introduced by Jon Bentley in 1975, which is still widely used for multidimensional searching. However, despite decades of research, current solutions have either exponential time or space complexity in d. This phenomenon is often referred to as the "curse of dimensionality." In recent years, several researchers have proposed methods to solve the time bottleneck by using approximation. These algorithms allow returning points that are within a factor of c times the distance of the nearest neighbor. The advantage of this approach is that the approximate nearest neighbor is often very close to the exact solution. Moreover, it is possible to find the exact nearest neighbor by efficiently enumerating all approximate neighbors and selecting the closest one. The paper focuses on one of the most widely used algorithms based on the concept of locality-sensitive hashing (LSH). The core idea is to choose hash functions that guarantee a higher collision probability for nearby points than for distant ones. By hashing the query point and retrieving the points stored in the corresponding bucket, one can find the nearest neighbor. LSH algorithms and their variants have shown effectiveness in various computational problems, including web clustering, computational biology, computer vision, computational chemistry, and computational linguistics. The code implementing these algorithms is available from the authors. For a more theoretical overview, refer to [24]. The paper's purpose is to present two main aspects: Section 2 discusses the basic idea and analysis of LSH algorithms, while Section 3 provides an overview of the currentThis paper presents an overview of efficient algorithms for the nearest neighbor problem, both approximate and exact. The goal is to preprocess a set of objects (e.g., images) so that, given a new query object, the algorithm can quickly return the closest object in the set. This problem is of great interest in various fields, including data compression, databases and data mining, information retrieval, image and video databases, machine learning, pattern recognition, and statistics. The paper is divided into two main parts. First, it provides an overview of a series of algorithms for the nearest neighbor problem based on the concept of locality-sensitive hashing (LSH). These algorithms have already found practical applications. Second, it describes recently discovered hash-based algorithms for d-dimensional Euclidean space. These algorithms are believed to be nearly optimal. The paper begins by defining the nearest neighbor problem. Given a set of n points, the goal is to build a data structure that, for any query point, returns the closest point in the set. This problem is particularly interesting when the points are in a d-dimensional space with a distance function, such as Euclidean distance. The features of objects (e.g., images) are often represented as points in R^d, and the distance metric is used to measure similarity between objects. The basic problem is then to index these features and perform similarity searches. When the dimension d is small (up to 10 or 20), efficient algorithms exist. One such data structure is the kd-tree, introduced by Jon Bentley in 1975, which is still widely used for multidimensional searching. However, despite decades of research, current solutions have either exponential time or space complexity in d. This phenomenon is often referred to as the "curse of dimensionality." In recent years, several researchers have proposed methods to solve the time bottleneck by using approximation. These algorithms allow returning points that are within a factor of c times the distance of the nearest neighbor. The advantage of this approach is that the approximate nearest neighbor is often very close to the exact solution. Moreover, it is possible to find the exact nearest neighbor by efficiently enumerating all approximate neighbors and selecting the closest one. The paper focuses on one of the most widely used algorithms based on the concept of locality-sensitive hashing (LSH). The core idea is to choose hash functions that guarantee a higher collision probability for nearby points than for distant ones. By hashing the query point and retrieving the points stored in the corresponding bucket, one can find the nearest neighbor. LSH algorithms and their variants have shown effectiveness in various computational problems, including web clustering, computational biology, computer vision, computational chemistry, and computational linguistics. The code implementing these algorithms is available from the authors. For a more theoretical overview, refer to [24]. The paper's purpose is to present two main aspects: Section 2 discusses the basic idea and analysis of LSH algorithms, while Section 3 provides an overview of the current