<p>Circle packings are arrangements of circles that satisfy specified tangency requirements. Many problems about the packing of circles and spheres occur in nature, particularly in material design and protein structure. Rigidity theory studies the realizations of graphs under edge length constraints. This paper tries to bridge classical circle packing problems with modern rigidity theory. We study the rigidity of circle packings representing a given planar graph under radii constraints. We provide sufficient conditions for the packing to be rigid in the first and second order. This gives us a sufficient condition to show a packing is rigid locally. These tools are particularly powerful in optimization problems. Then we will explore the difficulties of global rigidity and explain how the solutions to global rigidity can make progress on some longstanding open problems.</p>