In the past fifteen years, various formal models of concept learning have successfully been employed to answer the question of what types of concepts can be efficiently inferred from examples. The answer appears to be "only simple ones". Perhaps due to the ease of formal analysis, our investigations have focused on learning artificial, syntactically-described concepts in "sterile", knowledge-free environments. We discuss analogous results from the Literature on human concept learning (people don't do too well either), and review current theories as to how people are able to more effectively learn in the presence of background knowledge and the discovery of information via execution of tasks related to the concept acquisition process. We consider the formal modeling of such phenomena as an important challenge for learning theory.