We discuss statistical information theory, including divergences, entropy, statistical information, and related topics. We will demonstrate the necessity of a proper understanding of statistical information topics for the better development of novel, flexible, and well-behaved statistical methods. Moreover, several important open questions have been formulated. Part of the material has been presented during lectures on “Divergences and Statistical Decisions” and “Ill-posed Relations between Two Types of Information and between the Divergences and the Statistical Information” at the Stochastics Seminar of the University of Mannheim. The other parts address novel developments. In general, the topics relate to Fisher information, statistical divergences, and dynamical distributed systems.