Constraint programming is used to model and solve complex combina- torial problems. The modeling task requires some expertise in constraint programming. This requirement is a bottleneck to the broader uptake of constraint technology. Several approaches have been proposed to assist the non-expert user in the modelling task. This paper presents the basic architecture for acquiring constraint networks from examples classified by the user. The theoretical questions raised by constraint acquisition are stated and their complexity is given. We then propose Conacq, a sys- tem that uses a concise representation of the learner’s version space into a clausal formula. Based on this logical representation, our architecture uses strategies for eliciting constraint networks in both the passive acquisition context, where the learner is only provided a pool of examples, and the active acquisition context, where the learner is allowed to ask membership queries to the user. The computational properties of our strategies are analyzed and their practical effectiveness is experimentally evaluated.