Options and market making are recurring themes in Mathematical Finance. This thesis explores both topics with the ultimate goal of developing an options market making model for exchange-traded vanilla options. We start the derivation of closed-form optimal controls for an asset-agnostic market making model with multiple assets via an ergodic limit. We then investigate the intraday dynamics of options and its connection with spot volatility to gain insights on the high-frequency option price dynamics and on volatility and Greeks estimation. Finally, we develop a market making model for exchange-traded vanilla options that encompasses relevant features that we observe empirically. Closed-form solutions for the options market making model can be obtained via small time-to-horizon asymptotics. The optimal spreads in the small time-to-horizon regime allow us to empirically study options spreads and trading activity.