Summary: As communication networks grow, existing fault handling tools that involve global measures such as global time-outs or reset procedures become increasingly unaffordable, since their cost grows with the size of the network. Rather, for a fault handling mechanism to scale to large networks, its cost must depend only on the number of failed nodes (which, thanks to today's technology, grows much more slowly than the networks). Moreover, it should allow the nonfaulty regions of the networks to continue their operation even during the recovery of the faulty parts. This paper introduces the concepts fault locality and fault-locally mendable problems, which are problems for which there are correction algorithms (applied after faults) whose cost depends only on the (unknown) number of faults. We show that any input-output problem is fault-locally mendable. The solution involves a novel technique combining data structures and ``local votes'' among nodes, which may be of interest in itself.