Three different approaches to correlated electron systems are presented. (i)The single impurity Anderson model is solved by a semi-analytical approach based on the flow equation method. (ii)A numerically implementable Multi-scale Many-Body approach to strongly correlated electron systems is introduced. An extension to quantum cluster methods, it approximates correlations on any given length-scale commensurate with the strength of the correlations on the respective scale. (iii) The spectral properties of the one-dimensional Holstein and breathing polaron models using the self-consistent Born approximation are presented.