This thesis provides an in-depth investigation of effective non-Hermiticity and topology in many-mode, non-interacting, bosonic systems. It also establishes the extent to which one must move beyond the Hamiltonian, closed-system setting, in order to uncover signatures of genuine symmetry-protected topological (SPT) physics in "free" (mean-field) bosons. While SPT phases of free fermionic matter and their associated zero-energy boundary-localized modes have been thoroughly explored, similar physics in free bosonic systems still remains elusive. No fermionic counterpart exists for the...