The importance of erotetic inferences for scientific reasoning, and for reasoning and problem solving in general, can hardly be overestimated. The explanation of new phenomena, the discovery of new laws and theories, even the design and performance of experiments, all involve the derivation of questions. Notwithstanding their obvious importance, erotetic inferences have long been neglected. A recent central contribution in this respect is Wisniewski's theory of questions, which both generalizes and systematizes Hintikka's interrogative model. Wisniewski's theory provides a semantic explication of several erotetic concepts, of which the most interesting are question evocation, question generation and erotetic implication. The aim of this lecture is twofold. In the first part we will present a dynamic proof theory for question evocation. This proof theory will proceed in terms of an adaptive logic that is based on (an extension of) Classical Logic, and will enable one to infer different types of questions from a set of declarative sentences and/or other questions. We will show that this proof theory can be adjusted to capture the concept of erotetic implication. We will also show that the proof theory enables one to define the related concept of partial erotetic implication. The latter was not studied by Wisniewski, but opens interesting new perspectives (especially from the point of view of heuristics). In the second part we will discuss some alternative approaches and some extensions. First, we shall show that the results obtained in the first part can be reconstructed in terms of an epistemic logic that allows for expressions of the form "it is an open question ...". Next, we will present a semantic analysis of the concept "presently evoked". This analysis will proceed in terms of a block semantics. Finally, we shall discuss some open problems concerning the semantics of questions.