Recently there has been great progress in constructing moduli spaces of K-stable Fano Varieties, and there are many questions to ask about the geometry of these moduli spaces. The question I am considering is whether they are uniruled. My goal is to show that there are components of these moduli spaces that are general type, answering that question in the negative. I wish to do this by studying moduli spaces of vector bundles on curves, showing they are K-stable, and studying the components of the moduli space of K-stable Fano varieties that parametrize them.