The article discusses the main approaches in the development of quality management systems at domestic and foreign enterprises. The features inherent in each of the above schools of quality management are highlighted and considered. The analysis of the advantages and disadvantages of various approaches to the organization of the quality system at the enterprise is given. It is shown that the quality management of products and processes plays a key role in the organization of stable activities of business entities. The process approach reflects the mechanism of the quality management system in the enterprise. The main attention is focused on the main problems of the development of quality management systems in modern enterprises. The statistics of the implementation of the National Project «Labor Productivity», covering the implementation of measures to improve the quality of processes at Russian enterprises, are presented. The analysis of the main indicators is carried out and the assessment of the implementation of the payment is given relative to the current project. The conclusion is made about the propensity of modern domestic enterprises to introduce elements of «lean» production, and the main trends in the development of quality management systems are identified.