This paper studies the consumption-saving decisions of present-biased consumers. Building on Harris and Laibson (2013), I show that continuous-time methods allow for present bias to be tractably incorporated into incomplete markets models. First, I solve a workhorse Aiyagari-Bewley-Huggett model with present-biased consumers. The equilibrium with present bias features a larger mass of low-liquidity households and a higher aggregate marginal propensity to consume (MPC), but also a thicker right tail of high-wealth households. Second, I extend the model to include credit cards, illiquid assets, and naivete. In this rich economic environment I present closed-form expressions characterizing the effect of present bias on consumption, the demand for illiquid assets, and welfare. This welfare analysis specifies the channels through which present bias can matter for policy, and leads to what I call the present-bias dilemma: present bias has large welfare costs, but individuals have little ability to alleviate these costs without government intervention.