Contract theory is one of the most active fields of research in contemporary microeconomics. One of the reasons why it has been particularly popular in recent years may be the fact that many economists think that the incomplete contracts approach as pioneered by Grossman and Hart (1986) and Hart and Moore (1990) can help to answer important questions regarding the boundaries of the firm, which have been raised by Coase (1937) and more recently by Williamson (1985). In the meantime, the incomplete contract paradigm has been fruitfully applied to many relevant economic topics which are no longer restricted to the theory of the firm. However, several economic theorists still feel uncomfortable about important issues surrounding the incomplete contracts approach. Such concerns have lead some researchers to a renewed interest in the more traditional theory of complete contracts, which is closely related to the theory of implementation or mechanism design. This article complements existing surveys on contract theory in two ways. First, the surveys that I am aware of are of a quite technical nature and therefore difficult to access for readers who are not already specialists in the field. In contrast, while trying to be as rigorous as necessary, this paper presents all ideas verbally without any mathematical pyrotechnics. Second, instead of attempting to be exhaustive and to provide final answers, this paper is focused on some specific topics which received particular attention by researchers in recent years and puts emphasis on open questions that should be addressed in future research.