The ancient Greek amphitheaters and roofed odeia represent the earliest examples of acoustics utilized for enhancing theatrical and music performances over large public audiences, often up to 15,000 participants. Such an early achievement, more than 2000 years ago, was possibly crucial for the foundation of these performance-based art forms within the ancient Greek society and the eventual geographical spread of these buildings. Through the continuous evolution during the Roman era, via the Renaissance theaters and the modern concert halls, these specially constructed spaces allowed the performance-based art forms to be sustained and evolve as essential constituents of the western cultural heritage and civilization. We shall first consider some historical and architectural properties of these early performance spaces and then summarize their design principles and acoustic parameters. Acoustic properties were different for spaces used for theatrical and music performances: open-air theaters for drama were manly utilizing early reflections (e.g., up to 40 ms) to achieve perfect speech intelligibility for listener distances even beyond 60 m; in contrast, roofed-odeia had acoustics appropriate for music with prominent reverberation comparable to that of modern concert halls. The presentation will include auralization demos for important ancient theaters and odeia.