The Roman Theatre Museum lets you walk down through modern floors into the seating of a theatre cut into this hillside, and out onto its stage. Rome founded Olisipo on this hill, and in AD 57 the theatre was rebuilt in marble brought from the Alentejo and stone from the Sintra hills. The work was paid for by Caius Heius Primus, a former slave freed by an important family, who had grown rich and had his own name cut into the inscription across the stage front, beside the emperor Nero's.
For most of the two thousand years since, this was invisible. The theatre went out of use, the slope was built over, and Lisbon lived on top of it without knowing. Excavation has run in stages, so what you walk down into is the part that has been cleared rather than the whole building. The museum above was designed not to touch the ruin: modern floor and concrete stop wherever Roman stone begins, and the joins are visible as you descend. What you can stand inside is only the theatre. The rest of Roman Olisipo is still under the streets you walked in on.