The focus of this chapter concerns a critical question for psychology researchers interested in applying big data methods—what can Big Data and computational social science do to improve the likelihood that its research meets emerging criteria for robust and reliable psychological science? We begin by first describing what we believe are the characteristics of a robust Big Data science and some of the more significant challenges for meeting these demands. The remainder of the chapter then focuses on three issues related to scientific credibility that have been frequent topics of discussion in psychology (hypothesizing after results are known (HARKing), questionable research practices (QRPs), and replicability/reproducibility), describing their relevance to Big Data research, and offering recommendations for facilitating reliable and robust contributions of Big Data science to psychology.