The oil industry has recently started to deal with probabilistic approach. Risk or uncertainty analysis have become part of the petroleum engineer's job. A set of curves with the associated probability instead of one deterministic curve is provided by the reservoir engineers. In order to use reliable curves, they shall have a history matched model. Assisted History Matching usually uses optimization processes. The aim of the optimization is to find the minimum of an objective function that represents the quality of the model. In this way, one can find the best model. The keyword is exactly "best". Why to make so much effort to find the best if we know that it is still far from the truth. Indeed, the concept of "best" is not suitable for the probabilistic approach. This work discusses a functional history matching approach where an optimization process is no longer necessary. The functional history matching approach establishes that we have to look for a set of models that is above a level of quality according to the reservoir engineers. The method is quite simple. Among all possible models, we select those that have an objective function value under a pre-defined value. In this approach the discussion lies not in the optimization issues like local minimum, convergence, and rapidity, but in how the quality of the model is measured. The objective function that usually measures the quality must be very well defined. Not only to better take into account the historical data but also to be suitable to the purpose of the study. Infill drilling and new secondary recovery systems would probably require different objective functions. This work discusses the functional history matching approach coupled with uncertainty analysis. Usually very costly in terms of numerical simulations, uncertainty analysis can be done in this approach with simplified models (proxys). Different proxys were used -Surface Response Modeling (improved or not) and Artificial Neural Network. A simple synthetic case (PUNQ), and a real complex case (Brazilian onshore field) were used to illustrate the functional approach.