This paper presents the physical aspects of the acoustic properties of ancient theatres built by the ancient Greeks and Romans across the Mediterranean. Different theoretical approaches to assessing the sound field at the listener's position are summarised, alongside experimental and numerical results. The aim is to develop insight into why speech is remarkably intelligible in ancient theatres. The focus is on wave phenomena, particularly the scattering of sound by periodic surfaces and wedge diffraction. These phenomena, together with ordinary reflection, shape the sound in the theatre. A brief description in the language of partial differential equations is outlined, albeit without extensive technical and mathematical details. This article should therefore serve as an introduction to the subject.

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