It is a well-known that natural axiomatic theories are well-ordered by consistency strength. To investigate this phenomenon, we study a coarsening of the consistency strength order, namely, the \(\Pi^1_1\) reflection strength order. We prove that there are no descending sequences of \(\Pi^1_1\) sound extensions of \(\textrm{ACA}_0\) in this ordering. Accordingly, we can attach a rank in this order, which we call reflection rank, to any \(\Pi^1_1\) sound extension of \(\textrm{ACA}_0\). We prove that for any \(\Pi^1_1\) sound theory \(T\) extending \(\textrm{ACA}_0^+\), the reflection rank of \(T\) equals the proof-theoretic ordinal of \(T\). We will also describe recent research connecting iterated \(\Pi^1_1\) reflection with semantic \(\omega\)-model reflection. This is joint work with Fedor Pakhomov.