The behavior of real structures often exceeds the basic mechanics framework for various reasons. The non-deterministic nature of the structures, the presence of nonlinearities are taken into account to better understand the behavior of these structures in real cases operating in engineering. We propose here to give tools and address the conventional methods of engineering for introducing randomness and non-linearities in the systems, and to describe and more realistically the behavior of real structures and their optimization. Particular attention will also be paid to the engineer's process of defining a relevant mathematical model with regard to the experimental observations. These tools will be introduced through simple but significant examples. They will be borrowed from the industrial environment.