  Einstein's theory of general relativity models the physical universe using
spacetimes which satisfy Einstein's gravitational field equations. To date,
Einstein's theory has been enormously successful in modeling observed
gravitational phenomena, both at the astrophysical and the cosmological levels.
  The collection of spacetime solutions of Einstein's equations which have been
effectively used for modeling the physical universe is a very small subset of
the full set of solutions. Among this larger set, there are many spacetimes in
which strange phenomena related to time are present: There are solutions
containing regions in which determinism and the predictability of experimental
outcomes breaks down (the Taub-NUT spacetimes), and there others in which the
breakdown of determinism occurs everywhere (the G\"odel universe).
  Should the existence of these strange solutions lead us to question the
usefulness of Einstein's theory in modeling physical phenomena? Should it
instead lead us to seriously search for strange time phenomena in physics? Or
should we simply treat these solutions as anomalous (if embarrassing)
distractions which we can ignore?
  In this essay, after introducing some basic ideas of special and general
relativity and discussing what it means for a spacetime to be a solution of
Einstein's equations, we explore the use of spacetime solutions for modeling
astrophysical events and cosmology. We then examine some of the spacetime
solutions in which determinism and causal relationships break down, we relate
such phenomena to Penrose's "Strong Cosmic Censorship Conjecture", and finally
we discuss the questions noted above.
