For Warp drive. First, we get the math, then we get the physics and then we get the warp drive.
We not have all of the math and the physics but there has been progress on getting a better mathematical understanding of the physics of warping space and understanding how to possibly create warp drives.
There has been progress made on the math and physics of the warping space. In 1994, Miguel Alcubierre found a way to make them work in General Relativity. It is called the Alcubierre Drive. The idea was you contract space-time in front of you and expand it behind you, which moves you forward. There were still huge problems and it has barely moved from hand waving concept to mathematical hand waving. The amount of energy needed was like converting the mass of Jupiter into negative energy and concepts did not actually describe acceleration.
There have been experiments and efforts to try to make warping space into engineerable problems. However, new work mathematically defines mechanism for acceleration.