Whether we live in a spatially finite universe, and what its shape and size
may be, are among the fundamental long-standing questions in cosmology. These
questions of topological nature have become particularly topical, given the
wealth of increasingly accurate astro-cosmological observations, especially the
recent observations of the cosmic microwave background radiation. An overview
of the basic context of cosmic topology, the detectability constraints from
recent observations, as well as the main methods for its detection and some
recent results are briefly presented.