In this talk we report recent progress based on the seminal work of M. Waterman on the combinatorics of RNA secondary structures. We first discuss a new idea to obtain the generating function of pseudoknot RNA via the reflection principle. Then we discuss the singularity analysis of the latter and extend the results to the biologically relevant canonical RNA structures which satisfy certain minimum stack-length conditions. Then we observe that these ideas can be generalized for tertiary interactions and introduce the concept of tangles. Finally we introduce a new diagram algebra which is related to the Brauer centralizer algebra.