  Contraction theory is a mathematical framework for studying the convergence,
robustness, and modularity properties of dynamical systems and algorithms. In
this opinion paper, we provide five main opinions on the virtues of contraction
theory. These opinions are (i) contraction theory is a unifying framework
emerging from classical and modern works, (ii) contractivity is
computationally-friendly, robust, and modular stability, (iii) numerous
dynamical systems are contracting, (iv) contraction theory is relevant to
modern applications, and (v) contraction theory can be vastly extended in
numerous directions. We survey recent theoretical and applied research in each
of these five directions.
