Leadership is a kind of integrator of the problems of modern management science and practice, which leads to a continuing interest in the study of the personality of the leader and the models of his behavior and activities in modern society, in the management of organizations and processes. At the turn of the XX-XXI centuries, research in the field of leadership is very actively continuing, however, in general, it has changed its direction, shifting attention to the personality of the leader, the possibilities of his self-development and self-improvement for more effective leadership, internal motivation, the authenticity of the leader and his behavior, which was facilitated by the systemic crisis in business in developed countries, global problems of our time, the transition from the industrial economy to the knowledge economy. The article defines the fundamental differences in the leadership models of the industrial economy and the knowledge economy, and describes modern approaches to the study of leadership. It is revealed that modern leadership studies somehow develop the main directions of the study of leaders and leadership, set by classical concepts, but at the same time have significant distinctive trends that have formed in recent decades: the desire for collective leadership, the transition from transactional to transformational leadership, the development of leadership «deep» in the direction of self-motivation of the leader, a largely irrational approach to leadership.