A recent preprint of Abouzaid, Auroux, and Katzarkov constructs SYZ mirrors for certain "generalized conic bundles" over toric varieties. In this talk, after reviewing the construction, we examine their construction from the point of view of Homological Mirror Symmetry. I will describe joint work with Kazushi Ueda and Kwokwai Chan where we examine mirror symmetry for generalized conic bundles over $\mathbb{C}*$. We compute wrapped Floer homology of Lagrangian sections of the SYZ fibration and identify it with endomorphisms of certain line bundles on the mirror Calabi-Yau. We will also discuss compactly supported categories and categories of matrix factorizations as time permits.