In 1766, Euler conjectured that any closed spatial figure allows no change, as long as it is not ripped apart. The essence of this conjecture is indeed "rigidity": loosely speaking, a framework is rigid if any perturbation of it which preserves the lengths of the edges is induced by an isometry of the space. 

With such a simple definition, framework rigidity remains one of the most powerful tools in studying the lower bounds of face numbers of polytopes. In this talk, I will give basic definitions and results in the rigidity theory of frameworks, and then discuss its connection to the f-vector theory of polytopes. No preliminaries are required.