The simple, but general formal theory of fun and intrinsic motivation and creativity (1990-2010) is based on the concept of maximizing intrinsic reward for the active creation or discovery of novel, surprising patterns allowing for improved prediction or data compression. It generalizes the traditional field of active learning, and is related to old, but less formal ideas in aesthetics theory and developmental psychology. It has been argued that the theory explains many essential aspects of intelligence including autonomous development, science, art, music, and humor. This overview first describes theoretically optimal (but not necessarily practical) ways of implementing the basic computational principles on exploratory, intrinsically motivated agents or robots, encouraging them to provoke event sequences exhibiting previously unknown, but learnable algorithmic regularities. Emphasis is put on the importance of limited computational resources for online prediction and compression. Discrete and continuous time formulations are given. Previous practical, but nonoptimal implementations (1991, 1995, and 1997-2002) are reviewed, as well as several recent variants by others (2005-2010). A simplified typology addresses current confusion concerning the precise nature of intrinsic motivation.