The thesis deals with two different topics about the scaling limit of Markov Processes. In the first part of the thesis, we deduce the hydrostatic limit of three types of boundary driven exclusion processes with non-reversible boundary dynamics. In the second part, we study metastability of continuous time finite state Markov chains. For a sequence of Markov chains with certain assumptions on the jump rates, we present a recursive
procedure which permits to determine all valleys with different depths from shallow to deep, and the corresponding time scale.