In this chapter, we review recent results on the starving random walk (RW) problem, a minimal model for resource-limited exploration. Initially, each lattice site contains a single food unit, which is consumed upon visitation by the RW. The RW starves whenever it has not found any food unit within the previous \(\mathcal {S}\) steps. To address this problem, the key observable corresponds to the inter-visit time \(\tau _k\) defined as the time elapsed between the finding of the kth and the \((k+1)\) th food unit. By characterizing the maximum \(M_n\) of the inter-visit times \(\tau _0,\dots ,\tau _{n-1}\) , we will see how to obtain the number \(N_{\mathcal {S}}\) of food units collected at starvation, as well as the lifetime \(T_{\mathcal {S}}\) of the starving RW.