In the standard setting of online computation, the input is not entirely available from the beginning, but is revealed incrementally, piece by piece, as a sequence of requests. Whenever a request arrives, the online algorithm has to make immediately irrevocable decisions to serve the request, without knowledge on the future requests. Usually, the standard framework to evaluate the performance of online algorithms is competitive analysis, which compares the worst-case performance of an online algorithm to an offline optimal solution. In this thesis, we will study some new ways of looking at online problems. First, we study the online computation in the recourse model, in which the irrevocability on online decisions is relaxed. In other words, the online algorithm is allowed to go back and change previously made decisions. More precisely, we show how to identify the trade-off between the number of re-optimization and the performance of online algorithms for the online maximum matching problem. Moreover, we study measures other than competitive analysis for evaluating the performance of online algorithms. We observe that sometimes, competitive analysis cannot distinguish the performance of different algorithms due to the worst-case nature of the competitive ratio. We demonstrate that a similar situation arises in the linear search problem. More precisely, we revisit the linear search problem and introduce a measure, which can be applied as a refinement of the competitive ratio. Last, we study the online computation in the advice model, in which the algorithm receives as input not only a sequence of requests, but also some advice on the request sequence. Specifically, we study a recent model with untrusted advice, in which the advice can be either trusted or untrusted. Assume that in the latter case, the advice can be generated from a malicious source. We show how to identify a Pareto optimal strategy for the online bidding problem in the untrusted advice model.