People use social networks to share millions of stories every day, but these stories rarely become viral. Can we estimate the probability that a story becomes a viral cascade? If so, can we find a set of users that are more likely to trigger viral cascades? These estimation and maximization problems are very challenging since both rare-event nature of viral cascades and efficiency requirement should be considered. Unfortunately, this problem still remains largely unexplored to date. In this paper, given temporal dynamics of a network, we first develop an efficient viral cascade probability estimation method, ViCE, that leverages an special importance sampling approximation to achieve high accuracy, even in the cases of very small probability of influence. We then show that the most influential nodes in this model is NP-hard, and develop an efficient viral cascade probability maximization method, ViCEM, that maximizes a surrogate submodular function using a greedy algorithm. Experiments on both synthetic and real-world data show that ViCE can accurately estimate viral cascade probabilities using fewer samples than naive sampling by at least two orders of magnitude, and also ViCEM finds a set of users with higher viral cascade probability than alternatives. Additionally, experiments show that these algorithms are robust across different network topologies.