  The Borel covering property, introduced a century ago by E. Borel, is
intimately connected with Ramsey theory, initiated ninety years ago in an
influential paper of F.P. Ramsey. The current state of knowledge about the
connection between the Borel covering property and Ramsey theory is outlined in
this paper. Initially the connection is established for the situation when the
set with the Borel covering property is a proper subset of a $\sigma$-compact
uniform space. Then the connection is explored for a stronger covering property
introduced by Rothberger. After establishing the fact that in this case several
landmark Ramseyan theorems are characteristic of this stronger covering
property, the case when the space with this stronger covering property is in
fact $\sigma$-compact is explored.
