There are solutions to the spacetime metric within general relativity that allow for bubbles of space where the space itself moves along one dimension, propelled by a contraction of space in front and an expansion of space behind. Within this bubble (where a spacecraft would be) the space can be flat (no time dilation).

Such solutions were first proposed by Miguel Alcubierre in 1994. The original solutions required (a ludicrous amount of) negative energy to create these warp bubbles. Studies since then have proposed several solutions that both substantially reduce the energy requirements and allow for such spacetime manipulations through other means than negative energy/mass (EM effects e.g.).

Such technologies are mostly still theoretical, though there have been some potential experimental successes with warping space using EM, at least in the public sphere.

If these theories and experiments prove fruitful (or already have in secret) then moving between stars in a timely manner has the potential to be a part of the human experience, possibly within our lifetime.