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Multiway data, described by tensors, are common in real-world applications. For example, online advertising click logs can be represented by a three-mode tensor (user, advertisement, context). The analysis of tensors is closely related to many important applications, such as click-through-rate (CTR) prediction, anomaly detection and product recommendation. Despite the success of existing tensor analysis approaches, such as Tucker, CANDECOMP/PARAFAC and infinite Tucker decompositions, they are either not enough powerful to capture complex hidden relationships in data, or not scalable to handle real-world large data. In addition, they may suffer from the extreme sparsity in real data, i.e., when the portion of nonzero entries is extremely low; they lack of principled ways to discover other patterns — such as an unknown number of latent clusters — which are critical for data mining tasks such as anomaly detection and market targeting. To address these challenges, I used nonparametric Bayesian techniques, such as Gaussian processes (GP) and Dirichlet processes (DP), to model highly nonlinear interactions and to extract hidden patterns in tensors; I derived tractable variational evidence lower bounds, based on which I developed scalable, distributed or online approximate inference algorithms. Experiments on both simulation and real-world large data have demonstrated the effect of my propoaed approaches.