  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 $k^\text{th}$ and the $(k+1)^\text{th}$ 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.
