We investigate online nonlinear learning for several real life, adaptive signal processing and machine learning applications involving big data, and introduce algorithms that are both e cient and e ective. We present novel solutions for learning from the data that is generated at high speed and/or have big dimensions in a non-stationary environment, and needs to be processed on the y. We speci cally focus on investigating the problems arising from adverse real life conditions in a big data perspective. We propose online algorithms that are robust against the non-stationarities and corruptions in the data. We emphasize that our proposed algorithms are universally applicable to several real life applications regardless of the complexities involving high dimensionality, time varying statistics, data structures and abrupt changes. To this end, we introduce a highly robust hierarchical trees algorithm for online nonlinear learning in a high dimensional setting where the data lies on a time varying manifold. We escape the curse of dimensionality by tracking the subspace of the underlying manifold and use the projections of the original high dimensional regressor space onto the underlying manifold as the modi ed regressor vectors for modeling of the nonlinear system. By using the proposed algorithm, we reduce the computational complexity to the order of the depth of the tree and the memory requirement to only linear in the intrinsic dimension of the manifold. We demonstrate the signi cant performance gains in terms of mean square error over the other state of the art techniques through simulated as well as real data. We then consider real life applications of online nonlinear learning modeling, such as network intrusions detection, customers' churn analysis and channel estimation for underwater acoustic communication. We propose sequential and online learning methods that achieve signi cant performance in terms of detection accuracy, compared to the state-of-the-art techniques. We speci cally introduce structured and deep learning methods to develop robust learning algorithms. Furthermore, we improve the performance of our proposed online nonlinear learning models by introducing mixture-of-experts methods and the concept of boosting. The proposed algorithms achieve signi cant performance gain over the state-ofthe- art methods with signi cantly reduced computational complexity and storage requirements in real life conditions.