  This tutorial article introduces the physics of quantum information
scrambling in quantum many-body systems. The goals are to understand how to
precisely quantify the spreading of quantum information and how causality
emerges in complex quantum systems. We introduce a general framework to study
the dynamics of quantum information, including detection and decoding. We show
that the dynamics of quantum information is closely related to operator
dynamics in the Heisenberg picture, and, under certain circumstances, can be
precisely quantified by the so-called out-of-time ordered correlator~(OTOC).
The general behavior of OTOC is discussed based on several toy models,
including the Sachdev-Ye-Kitaev model, random circuit models, and Brownian
models, in which OTOC is analytically tractable. We introduce numerical
methods, including exact diagonalization and tensor network methods, to
calculate OTOC for generic quantum many-body systems. We also survey current
experimental schemes for measuring OTOC in various quantum simulators.
