In this chapter we will address the problem of polaron formation in different e-ph coupling models from a unifying variational point of view. This approach has the advantage of giving direct access to the ground state wavefunction making the understanding of the physical properties in the different regimes more transparent. Furthermore it allows us to study in a single framework the crossover between the weak coupling, where the electron moves coherently dragging a phonon cloud characterized by small lattice deformations involving a large area around the electron itself, and the strong coupling regime where the electron is self-trapped in the potential well created by the lattice deformations. It is worth noting that the use of strong and weak coupling is somehow not rigorous in the sense that, in different models, it can acquire different meanings. However, in this context, it is used in order to individuate the two asymptotic regimes that characterize the polaron physics. All the e-ph models discussed in this chapter are characterized by a linear coupling between the electron and the lattice displacements that are described by dispersion-less longitudinal optical phonons of frequency ω0. We will study models where the lattice displacement is coupled either to the electron density (Fröhlich and Holstein-like models) or to the electron hopping (SSH-like models) trying to emphasize the common points and investigating the role of the coupling range on the polaron properties.