In this talk, we discuss two classes of spaces of holomorphic functions on the unit disk D. First, the Model Spaces Ku, which arise as the invariant subspaces for the backward shift operator S* on the Hardy space H^2(D), given by S* f(z):=(f(z)-f(0))/z (z∈ D). The second class of spaces that we discuss are the harmonically weighted Dirichlet spaces D(m)$. The space D(m) consists of all analytic functions f on D such that D_m(f) :=∫_D |f'(z)|^2( ∫_{∂D} (1-|z|^2)/|z-\zeta|^2 dm(z)) dA(z) <∞. They are a generalization of the classical Dirichlet space D, and they arise naturally when studying the shift-invariant subspaces of D. After a brief introduction, we discuss sufficient and necessary conditions in order for the embedding Ku ↪ D(m) to hold. This work is related to the boundedness of the derivative operator acting on the model space Ku. This talk is based on joint work with Carlo Bellavita.