  The stochastic block model (SBM) is a random graph model with different group
of vertices connecting differently. It is widely employed as a canonical model
to study clustering and community detection, and provides a fertile ground to
study the information-theoretic and computational tradeoffs that arise in
combinatorial statistics and more generally data science.
  This monograph surveys the recent developments that establish the fundamental
limits for community detection in the SBM, both with respect to
information-theoretic and computational tradeoffs, and for various recovery
requirements such as exact, partial and weak recovery. The main results
discussed are the phase transitions for exact recovery at the
Chernoff-Hellinger threshold, the phase transition for weak recovery at the
Kesten-Stigum threshold, the optimal SNR-mutual information tradeoff for
partial recovery, and the gap between information-theoretic and computational
thresholds.
  The monograph gives a principled derivation of the main algorithms developed
in the quest of achieving the limits, in particular two-round algorithms via
graph-splitting, semi-definite programming, (linearized) belief propagation,
classical/nonbacktracking spectral methods and graph powering. Extensions to
other block models, such as geometric block models, and a few open problems are
also discussed.
