In this thesis, I develop and explore two novel models of how humans might be able to acquire high-level conceptual knowledge by performing probabilistic inference over a language of thought (LOT)– a space of symbolic and compositional mental representations sufficiently expressive to capture the meanings of human thoughts and utterances. These models and their associated learning algorithms are motivated by an attempt to provide an understanding of the algorithmic principles that might underlie a child’s ability to search the haystack of sentences in her language of thought to find the needle that corresponds to any specific concept. The first model takes advantage of the compositionality inherent to LOT representations, framing concept acquisition as program induction in a functional programming language; the Exploration-Compression algorithm this model motivates iteratively builds a library of useful program fragments that, when composed, restructures the search space, making more useful programs shorter and easier to find. The second model, the Infinite Knowledge Base Model (IKM), frames concept learning as probabilistic inference over the space of relational knowledge bases; the algorithm I develop for learning in this model frames this inference problem as a state-space search over abductive proofs of the learner’s observed data. This framing allows us to take advantage of powerful techniques from the heuristic search and classical planning literature to guide the learner. In the final part of this thesis, I explore the behavior of the IKM on several case studies of intuitive theories from the concept learning literature, and I discuss evidence for and against it with respect to other approaches to LOT models.