Abstract: To design successful and big comparative studies, such as online A/B testing experiments, causal inference and clinical trials, there are many important statistical challenges. In this talk, I will first discuss some related design issues of big experiments.  Then we will focus on how to balance many covariates in big comparative studies. To address this issue, the proposed method allocates the units sequentially and adaptively, using information on the current level of imbalance and the incoming unit's covariate.  With a large number of covariates or a large number of units, the proposed method shows  substantial advantages over the traditional methods in terms of the covariate balance and computational time, making it an ideal technique in the era of big data as well as online A/B testing experiments. Some real examples provide further evidence of the advantages of the proposed method. This talk is partially based on some joint researchs with Yichen Qin, Yang Li, Wei Ma and Fan Wang.