  Kuranishi structures were introduced to symplectic topology by Fukaya and Ono
and recently refined by Joyce, in order to extract homological data from
compactified moduli spaces of holomorphic maps in cases where geometric
regularization approaches such as perturbations of the almost complex structure
do not yield a smooth structure on the moduli space. We give a general survey
of regularization techniques in symplectic topology, pointing to some general
analytic issues, and discussing some specific topological issues of the
Kuranishi approach. In the main body of the paper we provide an abstract
framework of Kuranishi atlases which separates the analytic and topological
issues. Throughout, we focus on the most fundamental issues, which are already
present in applying virtual transversality techniques to moduli spaces of
holomorphic spheres without nodes or nontrivial isotropy. This is the
reinstated 2013 version of this survey and sample construction. A generalized
version of the topological theory is now available under 'The topology of
Kuranishi atlases' arxiv:1508.01844, with the survey parts and VMC construction
updated in 'The fundamental class of smooth Kuranishi atlases with trivial
isotropy' arxiv:1508.01560.
