In financial markets, a market maker is a market participant that continuously provide both buy and sell quotes for a single or multiple assets. This agent is crucial for maintaining the liquidity of the markets in which they participate. The profit of the market maker comes from the spread between these quotes. Tight spread implies more attractive prices and, hence, a flow of trades, at the cost of less profit per round-trip transaction. On the other hand, given that supply and demand change over time, the market maker has to dynamically control their quotes, otherwise they risk accumulating excessively high positive or negative positions in the traded asset, exposing them to market risk. In this talk, I will introduce the problem of optimal quotes for a market making strategy using optimal stochastic control theory. Then, I will expose the latest advancements in the literature and what challenges are involved when extending the models towards different asset classes.