Self-organizing teams are a common way of organizing teamwork in sectors related to modern technologies, especially in programming teams. Agile methods often promote and advocate such teams. One of the problems in this form of team organization is the issue of leadership, and particularly the relationship between vertical leadership - one person, and horizontal leadership - team members. In the literature on the subject, we can find traces of many concepts in such a broad area as the issue of leadership. However, several selected concepts allow us to capture an emerging feature in self-organizing teams which is the taking over of leadership functions by team members. Shared leadership, where the leadership function comes from team members, not from one appointed leader. Distributed leadership is where leadership in the organization is taken over voluntarily by individuals. Balanced leadership, where the vertical leader enables team members to take over leadership functions depending on the situation. The selected concepts presented here allow for a better understanding and research of the nature and phenomenon of leadership in self-organizing teams.