In this paper, we assess the impact of Airbnb on housing rents and prices in the city of Barcelona. Examining very detailed data on rents and both transaction and posted prices, we use several econometric approaches that exploit the exact timing and geography of Airbnb activity in the city. These include i) panel fixed-effects models, where we run multiple specifications that allow for different forms of heterogeneous time trends across neighborhoods, ii) an instrumental variables shift-share approach in which tourist amenities predict where Airbnb listings will locate and Google searches predict when listings appear, iii) event-study designs, and iv) finally, we present evidence from Sagrada Familia, a major tourist amenity that is not found in the city centre. Our main results imply that for the average neighborhood, Airbnb activity has increased rents by 1.9%, transaction prices by 4.6% and posted prices by 3.7%. The estimated impact in neighborhoods with high Airbnb activity is substantial. For neighborhoods in the top decile of Airbnb activity distribution, rents are estimated to have increased by 7%, while increases in transaction (posted) prices are estimated at 17% (14%).