Analyses of strong-interaction data consisting of level shifts, widths and yields in strange atoms of K⁻ mesons and Σ⁻ hyperons are reviewed. Recent results obtained by fitting to comprehensive sets of data across the periodic table in terms of density-dependent optical potentials are discussed. The introduction of density dependence generally improves significantly the fit to the data, leading to novel results on the in-medium hadron-nucleon t matrix t(ρ) over a wide range of densities up to central nuclear densities. A strongly attractive K⁻-nuclear potential of order 150–200 MeV in nuclear matter is suggested by fits to K⁻-atom data, with interesting possible repercussions on condensation and on the evolution of strangeness in high-density stars. The case for relatively narrow deeply bound K⁻ atomic states is made, essentially independent of the K⁻ potential depth. In view of the recently reported inconclusive experimental signals of deeply bound states, dynamical models for calculating binding energies and widths of -nuclear states are discussed. Lower bounds on the width, MeV, are established. For Σ⁻ atoms, the fitted potential becomes repulsive inside the nucleus, in agreement with recently reported (π⁻,K⁺) spectra from KEK, implying that Σ hyperons generally do not bind in nuclei. This repulsion significantly affects calculated compositions and masses of neutron stars.