  From the famous classical "simple man" model to the recent multichannel model
for polyatomic molecules, this tutorial will guide you through the several
landmarks in our understanding of high harmonic generation and high harmonic
spectroscopy. Our goal was to provide recipes and insights for modelling the
harmonic response in various regimes, from the single active electron regime
typical for noble gas atoms to the laser-driven attosecond hole dynamics in
polyatomics. We have tried to pay particular attention to both simple recipes
and their limitations, including the connection of real-valued classical and
complex-valued quantum times and velocities. In addition to physical pictures,
general approaches and their practical realizations, we have also tried to
discuss some of the sticky technical issues, such as the possibility to
factorize high harmonic response into the three steps of ionization,
propagation and recombination and practical ways to treat strong field
ionization, search for the saddle points of multi-dimensional integrals, deal
with poles arising in the quantum-mechanical integrands, remove divergences
appearing in approximate saddle point expressions, etc.
