Nowadays practical solutions of engineering problems involve model integrated computing. Model based approaches offer a very challenging way to integrate a priori knowledge into the procedure. Due to their flexibility, robustness, and easy interpretability, the application of soft computing (SC), in particular fuzzy models, may have an exceptional role at many fields, especially in cases where the problem to be solved is highly nonlinear or when only partial, uncertain and/or inaccurate data is available. Nevertheless, ever so advantageous their usage can be, it is still limited by their exponentially increasing computational complexity. At the same time, there are other soft computing approaches which can counteract the nonadvantageous aspects of fuzzy (in general SC) techniques. Anytime processing is the youngest member of the soft computing family. Systems based on this approach are flexible with respect to the available input data, time, and computational power. They are able to work in changing circumstances and can ensure continuous operation in recourse, data, and time insufficient conditions with guaranteed response time and known error. Thus, combining fuzzy and anytime techniques is a possible way to overcome the difficulties caused by the high and explosive complexity of the applied models and algorithms. The vagueness of the design procedure of the models in respect of the necessary complexity can be vanquished by model optimization and anytime mode of operation because the former can filter out the redundancy while the latter is able to adaptively cope with the available, usually imperfect or even missing information, the dynamically changing, possibly insufficient amount of resources and reaction time. This chapter deals with the history and advantageous aspects of anytime fuzzy systems.