The so-called "Above Threshold Ionization" (ATI), is a process in the course of which a quantum system (atom, molecule,...) absorbs more photons than strictly necessary for being ionized. Evidenced first in atoms in the presence of a strong IR laser field, it becomes feasible to observe it in the x-ray range, thanks to the advent of XFELs and harmonic-based sources. The objective of the tutorial is to review various aspects of the theoretical descriptions of the process, from the perturbative to the non-perturbative regimes, and from the low-frequency to the high-frequency ranges. Several issues related to "two-color" (IR-XUV) ionization recent experiments will be also addressed, if time permits.