This work concentrates on estimation and sampling aspects in slow mixing Markov Processes. When a process has slow mixing property, a large number of observations is needed before exploring the state space of the process properly. Empirical properties of finite sized samples from Markov processes need not reflect stationary properties. When empirical counts of samples eventually reflect the stationary properties, we say that the process has mixed. The contributions of this work revolve around interpretation of samples before mixing has occurred. In first part of the work, we deal with estimation of parameters of the process, while in the second part, we will show how the evolution of the samples obtained from the process can be exploited to identify subsets of state space which communicate well together. This insight will be translated into algorithmic rules for detecting communities in graphs.