An important objective of brain tumor modeling is to predict the progression of tumors so as to provide guidance about the best possible medical treatment to halt or slow the tumor's growth. Such computer models also provide a deeper insight into the physiology of tumors. In addition, one can study various what-if scenarios, for instance, investigating the response of tumors following the administration of a drug or a variety of drugs. Abrupt changes in growth rate can also be important for surgical decision-making. Despite increased interest in modeling techniques, relatively little progress has been made in improving such technologies. One problem is the limited data available from patients, typically 1 to 3 MRI (magnetic resonance imaging) sessions, from which one has to extrapolate the type of tumor so as to successfully predict its evolution over time. Here, the biological and clinical aspects of tumor growth and treatment with surgery, radiotherapy and drugs are discussed in the light of a patient with a brain tumor showing accelerated growth over time. Then, the contributions of mathematical modeling of tumor growth and effects of treatment are presented. Current tumor growth models can be roughly divided in three main categories, (i) cellular and microscopic models that emphasize isolated cell behavior, (ii) macroscopic models that concentrate on the development of cell density over time, and (iii) hybrid approaches that contain elements of both microscopic and macroscopic models. The mathematical theory that underlies these simulation methods is remarkably similar to the physical theory that forms the basis of protein modeling and molecular mechanics tools. A severe limitation of current models is that they are in fact not patient-specific at all.