Action potentials and associated Ca2+ influx can be followed by slow after-hyperpolarizations (sAHPs) caused by a voltage-insensitive, Ca2+-dependent K+ current. Slow AHPs are a widespread phenomenon in mammalian (including human) neurons and are present in both peripheral and central nervous systems. Although, the molecular identity of ion channels responsible for common membrane potential mechanisms has been largely determined, the nature of the channels that underlie the sAHPs in neurons, both in the brain and in the periphery, remains unresolved. This short review discusses why there is no clear molecular candidate for sAHPs.