Traditional learning to rank methods learn ranking models from training data in a {\it batch} and {\it offline} learning mode, which suffers from some critical limitations, e.g., poor scalability as the model has to be re-trained from scratch whenever new training data arrives. This is clearly non-scalable for many real applications in practice where training data often arrives sequentially and frequently. To overcome the limitations, this paper presents SOLAR --- a new framework of Scalable Online Learning Algorithms for Ranking, to tackle the challenge of scalable learning to rank. Specifically, we propose two novel SOLAR algorithms and analyze their IR measure bounds theoretically. We conduct extensive empirical studies by comparing our SOLAR algorithms with conventional learning to rank algorithms on benchmark testbeds, in which promising results validate the efficacy and scalability of the proposed novel SOLAR algorithms.