It is apparent that physics and numerics are strongly linked in every serious undertaking in computational mechanics. This is in particular pronounced when the matter of study excels through a very sophisticated, even sometimes tricky physical behaviour. Such a delicate characteristic is the trademark of shell structures, which are the most often used structural components in nature and technology. This outstanding position in the hierarchy of all structures is due to their curvature allowing to carry transverse loading in an optimal way by in-plane membrane actions, despite an often extreme slenderness. As typical for optimized systems their performance might be on the one hand excellent, but can also be extremely sensitive to certain parameter changes on the other hand. This prima donna like mechanical behaviour with all its sensitivities is of course carried over to any numerical scheme. In other words it is a fundamental precondition to understand the principle features of the load carrying mechanisms of shells before designing and applying any numerical formulation. The present study addresses this peculiar interrelation between physics and numerics. At first typical characteristics of shell structures are described; this include their benefits but also their extreme sensitivities. In the second part these aspects are reflected on related computational models and numerical procedures. This discussion is carried through a number of selected problems and examples. It need to be said that the paper is the outcome of a general plenary lecture addressing fundamental aspects rather than concentrating on a specific formulation or numerical scheme.