We highlight the main differences of available methods for the analysis of regression functions that are probably additive. First, definition and interpretation of most common estimators are discussed explaining the different ideas of modeling and what the procedures do to the data. Computational aspects are considered and simulations performed. Second, various statistics for testing additivity are introduced, accomplished with asymptotic theory, and finally compared. Again, detailed simulation studies are provided. A main focus is directed on the reliability of the methods. We found that the most striking differences lie in the different pre-smoothers that are used, but less in the construction each test.