Efficient online algorithms are developed to perform dictionary learning (DL) for the features lifted to a high-dimensional space via nonlinear mapping. Inspired by recent works on batch kernelized DL with promising performance for real-world learning tasks, two kernel DL formulations are put forth, amenable to online processing. The first formulation aims at faithfully representing the high-dimensional features in an unsupervised manner, while the the second one focuses on discriminative DL, where the dictionary is optimized for a specific supervised learning task. Motivated by Big Data processing applications, our algorithms are based on computationally efficient stochastic gradient descent variants. Numerical tests were performed to verify the convergence of the algorithms and to compare classification performances.