  This review aims at gathering the most relevant quantum multi-parameter
estimation methods that go beyond the direct use of the Quantum Fisher
Information concept. We discuss in detail the Holevo Cram\'er-Rao bound, the
Quantum Local Asymptotic Normality approach as well as Bayesian methods. Even
though the fundamental concepts in the field have been laid out more than forty
years ago, a number of important results have appeared much more recently.
Moreover, the field drew increased attention recently thanks to advances in
practical quantum metrology proposals and implementations that often involve
estimation of multiple parameters simultaneously. Since these topics are spread
in the literature and often served in a very formal mathematical language, one
of the main goals of this review is to provide a largely self-contained work
that allows the reader to follow most of the derivations and get an intuitive
understanding of the interrelations between different concepts using a set of
simple yet representative examples involving qubit and Gaussian shift models.
