The automated discovery of knowledge in databases is becoming increasingly important as the world's wealth of data continues to grow exponentially. Knowledge-discovery systems face challenging problems from real-world databases which tend to be dynamic, incomplete, redundant, noisy, sparse, and very large. This paper addresses these problems and describes some techniques for handling them. A model of an idealized knowledge-discovery system is presented as a reference for studying and designing new systems. This model is used in the comparison of three systems: CoverStory, EXPLORA, and the Knowledge Discovery Workbench. The deficiencies of existing systems relative to the model reveal several open problems for future research.