I will review some subtleties related to black hole quasinormal modes and a recently discovered connection between the greybody factors of black holes and the ringdown signal, their stability against small perturbations of the system, and how to use them for tests of gravity. I will also consider the greybody factors of ultracompact horizonless objects. They feature both low-frequency resonances and high-frequency, quasi-reflectionless scattering modes, which become purely reflectionless in the presence of symmetric cavity potentials. These high-frequency (quasi-)reflectionless scattering modes are directly connected to the echoes in the time-domain response of ultracompact objects or of black holes surrounded by matter fields localized at large distances.