The increasing penetration of renewable resources has changed the characteristics of power system and market operations, from one relying primarily on deterministic and static planning to one involving highly stochastic and dynamic operations. In such new operation regimes, the ability of adapting changing environments and managing risks arising from complex scenarios of contingencies is essential. To this end, an operation tool that provides probabilistic forecasting that characterizes the underlying probability distribution of variables of interest can be extremely valuable. A fundamental challenge in probabilistic forecasting for system and market operations is the scalability. As the size of system and the complexity of stochasticity increase, standard techniques based on direct Monte Carlo and machine learning techniques become intractable. This chapter outlines an alternative approach based on an online learning to overcome barriers of computation complexity.