This paper provides a brief overview of the stochastic modeling of variance swap curves. Focus is on affine factor models. We propose a novel drift parametrization which assures that the components of the state process can be matched with any pre-specified points on the variance swap curve. This should facilitate the empirical estimation for such stochastic models. Moreover, sufficient and yet flexible conditions that guarantee positivity of the rates are readily available. We finally discuss the relation and differences to affine yield-factor models introduced by Duffie and Kan. It turns out that, in contrast to variance swap models, their yield factor representation requires imposing constraints on systems of nonlinear equations that are often not solvable in closed form.