During the last fifteen years, a growing number of researchers in many disciplines ranging from computer science and AI to urban studies, communication, and digital humanities have big data methods for the study of culture. This work has generated many fascinating insights but also led to many questions. In my talk, I want to discuss what I see as some of the biggest challenges in looking at culture with computers, and think about the ways to address them. Why do we often approach cultural data using ideas developed in the 18th and 19th century, before digital computers and big data? Can we think about cultures without using categories? What does AI can see in cultural artifacts, and what it remains blind to? The presentation draws on my new book "Cultural Analytics" published by The MIT Press in October 2020 (https://mitpress.mit.edu/books/cultural-analytics (Links to an external site.)).