Lie algebroids are the infinitesimal counterpart of Lie groupoids, which generalize how we can talk about symmetries of smooth manifolds. Unlike Lie algebras, not every Lie algebroid can be integrated to a Lie groupoid, though Rui Loja Fernandes and Marius Crainic have recently given the conditions under which a Lie algebroid may be integrated. Poisson geometry investigates smooth manifolds $M$ with a certain Lie algebra structure on the ring of smooth functions $C^{\infty}(M)$. In this talk, I will describe the connection between these two subjects, and how knowing when a Lie algebroid is integrable tells us something about Poisson (and symplectic) geometry.