Natural data erupting directly out of various data sources, such as text, image, video, audio, and sensor data, comes with an inherent property of having very large dimensions or features of the data. While these features add richness and perspectives to the data, due to sparsity associated with them, it adds to the computational complexity while learning, unable to visualize and interpret them, thus requiring large scale computational power to make insights out of it. This is famously called “curse of dimensionality.” This chapter discusses the methods by which curse of dimensionality is cured using conventional methods and analyzes its performance for given complex datasets. It also discusses the advantages of nonlinear methods over linear methods and neural networks, which could be a better approach when compared to other nonlinear methods. It also discusses future research areas such as application of deep learning techniques, which can be applied as a cure for this curse.