Automatic Hand Gesture Recognition has become more important in recent years. Due to an increasing number of the deaf and hearing impaired, the use of a variety of non-contact-based applications and devices has also been increased. With the development of modern technology, it also plays a key role in the human-computer interaction systems. Sign language is the main instrument of communication among the deaf, the hearing impaired and the non-verbal. However, there are barriers for these groups in their daily interaction with people who do not understand any sign language. The recent studies in algorithm analysis and computer vision have led to the development of innovative efficient and accurate gesture recognition methods. Since HGR is the basis for sign language analysis, this paper is devoted to conducting the literary survey of hand gesture detection and recognition methods and algorithms, existing sign languages and their applications. The results of this paper can be summarized as following: artificial neural networks, which use advanced methods and algorithms for hand gesture detection and recognition, is the most useful classifier for the recognition of Kazakh Sign Language. In this paper, about 70 references published from 2012 to 2021 were reviewed for identifying common methods for hand gesture recognition.