This paper reviews theoretical warp-drive spacetimes as mechanisms for manipulating space-time curvature to enable rapid interstellar travel. Starting from theAlcubierre metric, we compare subsequent models that aim to reduce exotic energyrequirements or improve physical plausibility. We evaluate energy conditions, stability, control, and detectability, and summarize experimental proposals. While newermetrics mitigate some constraints, substantial theoretical and experimental challengesremain. We conclude with open problems and near-term research directions.