This paper surveys existing and past research on brain-computer interfaces (BCI) for implicit human-computer interaction. A novel way of using BCI has indeed emerged, which proposes to use BCI in a less explicit way : the so-called "passive" BCI. Implicit BCI or passive BCI refers to BCI in which the user does not try to control his brain activity. Thus the brain activity is assimilated to an input and can be used to adapt the application to the user's mental state. In this paper, we first study "implicit interaction" in general and recall its main applications. Then, we make a survey of existing and past research on brain-computer interfaces for implicit human-computer interaction. It seems indeed that BCI can be used in many applications in an implicit way, such as for adaptive automation, affective computing, or for video games. In such applications, BCI based on implicit interaction was often reported to improve performance of either the system or the user, or to introduce novel capacities based on mental states.