This paper is concerned with Markov processes for computing page importance. Page importance is a key factor in Web search. Many algorithms such as PageRank and its variations have been proposed for computing the quantity in different scenarios, using different data sources, and with different assumptions. Then a question arises, as to whether these algorithms can be explained in a unified way, and whether there is a general guideline to design new algorithms for new scenarios. In order to answer these questions, we introduce a General Markov Framework in this paper. Under the framework, a Web Markov Skeleton Process is used to model the random walk conducted by the web surfer on a given graph. Page importance is then defined as the product of two factors: page reachability, the average possibility that the surfer arrives at the page, and page utility, the average value that the page gives to the surfer in a single visit. These two factors can be computed as the stationary probability distribution of the corresponding embedded Markov chain and the mean staying time on each page of the Web Markov Skeleton Process respectively. We show that this general framework can cover many existing algorithms including PageRank, TrustRank, and BrowseRank as its special cases. We also show that the framework can help us design new algorithms to handle more complex problems, by constructing graphs from new data sources, employing new family members of the Web Markov Skeleton Process, and using new methods to estimate these two factors. In particular, we demonstrate the use of the framework with the exploitation of a new process, named Mirror Semi-Markov Process. In the new process, the staying time on a page, as a random variable, is assumed to be dependent on both the current page and its inlink pages. Our experimental results on both the user browsing graph and the mobile web graph validate that the Mirror Semi-Markov Process is more effective than previous models in several tasks, even when there are web spams and when the assumption on preferential attachment does not hold.