Online problems are those in which the instance is not given as a whole but by parts named requests. They arrise naturaly in computer science. Several examples are given such as ski rental problem, the server problem and the coloring problem. The performance of the online algorithms is analized in terms of the ratio between the cost of the algorithm and the cost of the optimal offline. This ratio is called the competitive ratio. Several models of online algorithms are described. They are deterministic algorithms, randomized algorithms and algorithms with advice. We present several upper and lower bounds for the competitive ratio in a particular case of the k-server problem. We review the known bounds for the coloring problem in the diferent models. We present a new model, the randomized adversary. For this model we present an upper bound and a restricted lower bound. Finally we conjecture an unrestricted lower bound and we present several approaches to the result
