The extreme values and exceedances above a high level u of a continuous Gaussian process will be reviewed for stationary and non- stationary cases. We focus on exact asymptotic laws as the level u tends to ?. Then we consider clusters of such exceedances which may occur de- pending on the high level u. We show that different types of clusters can be observed. The pattern depends on the underlying correlation function of the Gaussian process. Finally we talk on exceedances in relation of a random environment where the level u is replaced by a random boundary function.