  We review geometrical properties of a static spacetime $(M,g)$, including
geodesic completeness, causality, standard splittings, compact $M$, closed
geodesics and geodesic connectedness. We pay special attention to the critical
quadratic behavior at infinity of the coefficients $\beta$, $\beta^{-1}$
($\beta = -g(K,K)$, being $K$ a timelike irrotational Killing vector field),
which essentially control completeness, causality and geodesic connectedness.
Recent references are specially discussed.
