We discuss some non-symmetric distances that naturally arise in C*-algebras and demonstrate their utility in simplifying and generalizing certain order theoretic aspects of C*-algebra theory. For example, we outline how to use them to extend the C*-algebra semicontinuity theory of Akemann, Brown and Pedersen to more general ordered Banach spaces. We also show how they provide a new perspective on the norm/quantum filters in C*-algebras introduced by Farah and Weaver.