Using a Lanczos method, we study the spectra of Heisenberg chains with spin S= 1, 3/2, 2, 5/2, and 3, as a function of the anisotropy parameter λ and the number of sites of the chain. We use periodic, twisted, and open boundary conditions. We found that for all values of the spin when-1≤ λ≤ 0, these models are massless with critical behavior described by a conformal theory with central charge c= 1. We discuss the whole operator content. In particular, we found that the critical exponent η x follows the behavior η x=(π-γ)/2πS and η z= 2 where γ= cos− 1 (λ). For λ> 0, our results indicate that the S= 1 model is massive, while for S> 1, the massless behavior characterized by the critical exponents described above continues up to λ= λ*(S). For λ*< λ≤ 1, our results are consistent with a massive phase for the integer-spin models and a massless phase with a rapid variation of the critical exponents for the half-integer-spin models.