Abstract: We introduce and study a family of online metric problems with long-term constraints. In these problems, an online player makes decisions $\mathbf{x_t}$ in a metric space $(X,d)$ to simultaneously minimize their hitting cost $f_t( \mathbf{x_t} )$ and switching cost as determined by the metric. Over the time horizon $T$, the player must satisfy a long-term demand constraint $\sum_{t} c(\mathbf{x_t}) \geq 1$, where $c(\mathbf{x_t})$ denotes the fraction of demand satisfied at time $t$. Such problems can find a wide array of applications to online resource allocation in sustainable energy/computing systems. We devise optimal competitive and learning-augmented algorithms for specific instantiations of these problems, and further show that our proposed algorithms perform well in numerical experiments.