||One of central tasks in the study of Schrodinger Cocycles is to understand the properties of the spectrum. With the help of dynamical method, a lot of results have been obtained on the spectrum of one-dimensional quasi-periodic (q-p) Schrodinger operators. In particular, the Lyapunov Exponent (LE) plays a key role. In this talk, we first introduce the relation between LE and spectrum. Then we review the results on the properties of LE for analytic cases and their applications on the study of spectrum. Finally, we report recent advances on smooth cases, from which one may find that dynamical method has its own advantages for studying 1-dim q-p Schrodinger operators.