  Questions such as whether we live in a spatially finite universe, and what
its shape and size may be, are among the fundamental open problems that high
precision modern cosmology needs to resolve. These questions go beyond the
scope of general relativity (GR), since as a (local) metrical theory GR leaves
the global topology of the universe undetermined. Despite our present-day
inability to predict the topology of the universe, given the wealth of
increasingly accurate astro-cosmological observations it is expected that we
should be able to detect it. An overview of basic features of cosmic topology,
the main methods for its detection, and observational constraints on
detectability are briefly presented. Recent theoretical and observational
results related to cosmic topology are also discussed.
