  Over the last decade several positive definite kernels have been proposed to
treat spike trains as objects in Hilbert space. However, for the most part,
such attempts still remain a mere curiosity for both computational
neuroscientists and signal processing experts. This tutorial illustrates why
kernel methods can, and have already started to, change the way spike trains
are analyzed and processed. The presentation incorporates simple mathematical
analogies and convincing practical examples in an attempt to show the yet
unexplored potential of positive definite functions to quantify point
processes. It also provides a detailed overview of the current state of the art
and future challenges with the hope of engaging the readers in active
participation.
