The paper gives an overview of Estonian dialogue corpus. The corpus currently includes dialogues of two kinds - recordings of spoken conversations, and dialogues collected by Wizard of Oz technique. We have worked out a typology of dialogue acts and are annotating them in our corpus. Some problems of determining of dialogue acts are considered, among them different kinds of questions. We are interested in information-seeking dialogues first of all, and our further aim is to develop a dialogue system which can interact with a user in Estonian following norms and rules of natural human communication.