Topological phases, both single-particle and many-body, are often formulated through momentum-space invariants, many of which rely on the presence of a spectral gap. However, disorder and gapless spectra can make these conventional approaches difficult to apply. The spectral localizer provides an alternative real-space framework for defining and characterizing topology in such settings. By combining the Hamiltonian with position operators, it constructs a pseudospectrum that can identify topologically protected states while simultaneously providing a measure of their spectral stability. The spectral localizer has been successfully applied to a variety of single-particle systems, including disordered and gapless systems. In this seminar, I will present recent work extending the spectral localizer to many-body systems. Our construction provides a general pseudospectral framework for identifying topologically protected states throughout the many-body spectrum. We have used this framework to identify candidates for quantum many-body scarring in both an interacting chiral bosonic chain and the PXP model, demonstrating that the approach is not tied to a particular microscopic mechanism for scarring. The many-body spectral localizer thus provides new insight into the structure and stability of these anomalous ETH-violating states, while offering a quantitative measure of their stability. Finally, I will discuss the implications of this framework for quantum error-correcting codes constructed from quantum many-body scar subspaces.