  Most elementary behaviors such as moving the arm to grasp an object or
walking into the next room to explore a museum evolve on the time scale of
seconds; in contrast, neuronal action potentials occur on the time scale of a
few milliseconds. Learning rules of the brain must therefore bridge the gap
between these two different time scales.
  Modern theories of synaptic plasticity have postulated that the co-activation
of pre- and postsynaptic neurons sets a flag at the synapse, called an
eligibility trace, that leads to a weight change only if an additional factor
is present while the flag is set. This third factor, signaling reward,
punishment, surprise, or novelty, could be implemented by the phasic activity
of neuromodulators or specific neuronal inputs signaling special events. While
the theoretical framework has been developed over the last decades,
experimental evidence in support of eligibility traces on the time scale of
seconds has been collected only during the last few years.
  Here we review, in the context of three-factor rules of synaptic plasticity,
four key experiments that support the role of synaptic eligibility traces in
combination with a third factor as a biological implementation of neoHebbian
three-factor learning rules.
