Globalization of capital markets and the transition to market relations have made the development of the systems of (financial) accounting and audit activity urgent in Russia. Moreover, these systems should correspond to international standards. The use of International Standards on Auditing is regulated at the legislative level. The strategy of gradual convergence of the federal (national) accounting standards with the requirements of international standards is also entrenched. Thus, we may conclude that the application of international standards on accounting and auditing in Russia is rather an existing objective reality than a question of future concern. However, the development of audit in Russia for the recent twenty years has had its own peculiarities caused by significant public intervention, increasing concentration at the market of audit services due to the quantitative reduction of entities providing audit services, strengthening of price competition due to the development of the procurement system, the development of related and other services, the low demand for initiative audit. Correspondingly, the purpose of the research is to determine the trajectory of audit activity improvement on the basis of formation retrospective analysis and also on the basis of audit market development in Russia and abroad in terms of Russian economy digitalization including the transformation of the legislative regulation system and auditing practice. The statements and conclusion made in the article are based on the result analysis of the first large-scale questionnaire of audit service market. The survey was a part of the research "Analysis of business activity in the market of audit services in 2015-2016" conducted by the Financial Research Institute of the Ministry of Finance of the Russian Federation. The study is also based on a critical comprehension of the current legislative and other official documents regulating audit activities in the Russian Federation. The novelty of the research is to provide an original interpretation of the key trends of audit market development, of the changes in the field of auditing technologies and to justify the modification of requirements to auditors taking into account the contemporary practice of corporate management. The following negative trends that require the development and implementation of additional adaptation mechanisms of audit market development in Russia have been distinguished: 1) low demand for initiative audit due to unwillingness of customers to perceive the importance and value of auditing and auditors; 2) insufficient demand for services related to confirmation of reliability of accounting (financial) statements; 3) lack of ethics of civilized competition at the market of audit services. Further studies will be devoted to the elaboration of practical guidance on audit service market development in Russia. The guidance will be based on international practice and International Standards on Auditing.