It appears that the warp drive engine is beginning to take the steps out of the science fiction realm into the field of physics research. A new paper has suggested the mathematics to form the basis for a theory of warp drive engines. It describes the structure of the fields around the engine and how they react with the space-time continuum. It suggests that it is possible to travel faster than light but the people inside the warp drive bubble would experience time as normal for them, whilst to outside observers they would be taken out of the space-time continuum. This wouldn't conflict with Eisteinian relativity because they wouldn't be inside the bounds of the space-time continuum when they went FTL. However that only applies if Einsteins theories of relativity are correct and they may not be.
It's quite an interesting and exciting development and will be interesting to see how it develops. If they manage to get it past the theoretical stage and look at building an actual engine, the research, experimentation and engineering will be a huge undertaking.
Sabine Hossenfelder is a theoretical physicist who specialises in quantum gravity. She works at the Frankfurt Institute for Advanced Research.