This paper provides a theoretical rationale for the observed structure of boards, the size and the allocation of board members to monitoring committee (or outside director) and advising committee (or inside director). Also, this paper addresses a new question, a relationship between the quality of a CEO and the board structure. In my model, (1) the monitoring is to ?nd precise information for the quality of a CEO, (2) the impact of advising by boards increases with the quality of a CEO (complementarity), and (3) there is "size (capital)-skill complementarity" on the role of a CEO. My model suggests that the size of boards increases with the size of a ?rm. The size of board is larger where the ?rms face less uncertainty if the uncertainty decreases the informational gain by boards. Finally, when the CEO is expected to be good, the ?rms with more uncertainty are more likely to have small boards. Given the size of boards, the ?rms with more uncertainty and with talented CEOs allocate the more (less) directors to the advising (monitoring) committee. These predictions well explain the observed variations on boards.