This collection of studies leverages digital trace data to explore human migration, cultural similarity across countries, and online behavior in algorithmically mediated platforms. By analyzing platforms such as Facebook, Wikipedia, and TikTok, the research uncovers patterns and connections often overlooked or delayed by traditional methods. In the context of culture and migration, two studies leverage Facebook data to measure cultural similarity between countries and demonstrate the influence of cultural similarity on migration flows. Another study highlights the innovative use of Wikipedia data as a tool to track mass migration flows, offering real-time insights into population movements, particularly during crises like conflicts and wars. These studies primarily rely on the use of Application Programming Interface (API) for data access. However, as social media platforms increasingly restrict access to their data, alternative approaches like data donation, facilitated by GDPR, offer new opportunities for data collection. The final study leverages TikTok user-donated data to evaluate the predictability of user engagement with short-form videos, highlighting the potential of data donation for research. Together, these studies showcase the potential of digital trace data in advancing knowledge across social science and computational fields.