Metric and differential geometry are the main tools for studying sub-Riemannian geometries. Metric geometry provides the foundation for understanding distances, geodesics, and intrinsic geometric properties in sub-Riemannian manifolds, including the broader context of Carnot-Carathéodory spaces. Differential geometry is central and indispensable in sub-Riemannian geometry. It provides the mathematical framework for studying fundamental geometric objects such as tangent bundles and vector fields. It allows for analyzing the geometric interpretation of the sub-Riemannian distance as the minimization of a cost functional. This geometric cost functional can be viewed in metric and differential geometry as a length functional defined on curves.