  Quadratic nonlinear processes are currently exploited for frequency comb
transfer and extension from the visible and near infrared regions to other
spectral ranges where direct comb generation cannot be accomplished. However,
frequency comb generation has been directly observed in continuously-pumped
quadratic nonlinear crystals placed inside an optical cavity. At the same time,
an introductory theoretical description of the phenomenon has been provided,
showing a remarkable analogy with the dynamics of third-order Kerr
microresonators. Here, we give an overview of our recent work on $\chi^{(2)}$
frequency comb generation. Furthermore, we generalize the preliminary
three-wave spectral model to a many-mode comb and present a stability analysis
of different cavity field regimes. Although at a very early stage, our work
lays the groundwork for a novel class of highly efficient and versatile
frequency comb synthesizers based on second-order nonlinear materials.
