  A brief overview of some open questions in general relativity with important
consequences for causality theory is presented, aiming to a better
understanding of the causal structure of the spacetime. Special attention is
accorded to the problem of fundamental causal stability conditions. Several
questions are raised and some of the potential consequences of recent results
regarding the causality problem in general relativity are presented. A key
question is whether causality violating regions are locally allowed. The new
concept of almost stable causality is introduced; meanwhile, related conditions
and criteria for the stability and almost stability of the causal structure are
discussed.
