big list - What are the next generation physics experiments?

The LHC and LIGO are two recent examples of hugely ambitious experiments in fundamental physics, both of which took decades to develop.

What are the next major experiments currently being planned and developed? What will they measure? What impact are they expected to have? And when are they expected to go live?

One example:

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  eLISA due 2034

  
  

  Developed by the ESA, eLISA will be the first dedicated space-based gravitational wave detector. Consisting of three probes spanning millions of kilometres, it will provide a hugely more accurate window to gravitational waves.

  
  

  Possible signal sources: the usual GW stuff, the early phase of the big bang, and even speculative objects like cosmic strings.

  
  

I suggest, at some point, we collate all of the answers into a single community post.