Problem definition: Sequential experiments that are deployed in a broad range of practices are characterized by an exploration-exploitation trade-off that is well understood when in each time period feedback is received only on the action that was selected in that period. However, in many practical settings, additional information may become available between decision epochs. We study the performance that one may achieve when leveraging such auxiliary information and the design of algorithms that effectively do so without prior knowledge of the information arrival process. Methodology/results: Our formulation considers a broad class of distributions that are informative about rewards from actions and allows auxiliary observations from these distributions to arrive according to an arbitrary and a priori unknown process. When it is known how to map auxiliary observations to reward estimates, we characterize the best achievable performance as a function of the information arrival process. In terms of achieving optimal performance, we establish that upper confidence bound and Thompson sampling algorithms possess natural robustness with respect to the information arrival process, which uncovers a novel property of these popular algorithms. When the mappings connecting auxiliary observations and rewards are a priori unknown, we characterize a necessary and sufficient condition under which auxiliary information allows performance improvement and devise an adaptive policy (termed 2UCBs) that guarantees near optimality. We use a data set from a large media site to analyze the value that may be captured by leveraging auxiliary observations in the design of content recommendations. Managerial implications: Our study highlights the importance of utilizing auxiliary information in the design of sequential experiments and characterizes how salient features of the auxiliary information stream impact performance. Our study also emphasizes the risk in processing auxiliary information using nonadaptive approaches that are predicated on correct interpretation of this information, as opposed to deploying flexible, adaptive methods.