Discovering useful models capturing regularities of natural phenomena or complex systems until recently was almost entirely limited to finding formulae fitting empirical data. This worked relatively well in physics, theoretical mechanics, and other areas of science and engineering. However, in social sciences, market research, medicine, pharmacy, molecular biology, learning and perception, and in many other areas, the complexity of the natural processes and their common lack of analytical smoothness almost totally exclude the use of standard tools of mathematics for the purpose of data-based modeling. A fundamentally different approach is needed in those areas. The availability of fast data processors creates new possibilities in that respect. This need for alternative approaches to modeling from data was recognized some time ago by researchers working in the areas of neural nets, inductive learning, rough sets, and, more recently, data mining. The empirical models in the form of data-based structures of decision tables or rules play similar roles to formulas in classical analytical modeling. Such models can be analyzed, interpreted, and optimized using methods of rough set theory.