There is a rumbling debate over the impact of gentrification: presumed gentrifiers have been the target of protests and attacks in some cities, while they have been welcome as generators of new jobs and taxes in others. Census data fails to measure neighborhood change in real-time since it is usually updated every ten years. This work shows that Airbnb data can be used to quantify and track neighborhood changes. Specifically, we consider both structured data (e.g., number of listings, number of reviews, listing information) and unstructured data (e.g., user-generated reviews processed with natural language processing and machine learning algorithms) for three major cities, New York City (US), Los Angeles (US), and Greater London (UK). We find that Airbnb data (especially its unstructured part) appears to nowcast neighborhood gentrification, measured as changes in housing affordability and demographics. Overall, our results suggest that user-generated data from online platforms can be used to create socioeconomic indices to complement traditional measures that are less granular, not in real-time, and more costly to obtain.