Researchers have found online social networks a goldmine for research into various aspects of social behavior and interpersonal communication. For example, observing social interaction between individuals and their engagement in conversations, or performing sentiment analysis on these communications, is often carried out for research in a number of disciplines such as health, sociology, or politics. Such studies introduce many challenges for conducting research in a responsible manner. Data may be repurposed or cross-correlated in ways that participants may not have anticipated or desired, private information may be collected, or legal requirements may not be met. This chapter explores some of the challenges and dilemmas faced by industry, academia, regulators, privacy advocates, and ultimately the individuals using these services. It discusses the pros and cons of the collection, analysis, and archiving of personal data for digital research. The chapter concludes by discussing theoretical and practical approaches that target these dilemmas.