### 1.2 Plan of this review

Faced with more material to review, we have attempted to make this update shorter and more
systematic than the original 1999 version [102]. We begin with the abstract theory in Section 2. Since 1999,
progress on the theory side has mainly been made on the global spacetime structure of the critical solution
and cosmic censorship in the spherical scalar field model. We have included this new material in an enlarged
Section 3 on the spherical scalar field, although we hope it will turn out to be sufficiently generic to merit
inclusion in Section 2. Nonspherical perturbations of the spherical scalar field are also discussed in
Section 3.
In Section 4 we review the rich phenomenology that has been found in many other systems restricted to
spherical symmetry. Numerical work in spherical symmetry has proliferated since 1999, but we have tried to
keep this section as short as possible. There has been less progress in going beyond spherical symmetry than
we anticipated in 1999, even though we continue to believe that important results await there. What is
known today is summarised in Section 5.

The reader unfamiliar with the topic is advised to begin with either Sections 2.1, 2.2, and 2.3, which
give the key theory of universality, self-similarity and scaling, or Sections 3.1 and 3.2, which describe the
classic example, the massless scalar field.

This review is limited to numerical and theoretical work on phenomena at the threshold of black hole
formation in 3+1-dimensional general relativity. We report only briefly on work in higher and lower
spacetime dimensions and non-gravity systems that may be relevant as toy models for general relativity. We
exclude other work on self-similarity in general relativity and work on critical phenomena in other areas of
physics.

Other reviews on the subject are [129], [15], [96], [100], [50], [51], [33], [102], [156]. The 2002
review [105] by Gundlach gives more detailed explanations on some of the basic aspects of the
theory. A review of the role of self-similarity in the formation of singularities in evolutionary
PDEs in general is [71]. Update