To follow up on the setup-less SNARKs, the idea is to create concretely efficient probabilistically checkable proofs. These are proof systems first pioneered ~25 years ago, and contain a lot of elegant mathematics but unfortunately to this day they are highly impractical. However, Ale has been doing a lot of work on bringing these systems into the realm of practical feasibility, and the next few years in this field will be super exciting.
The additional benefit of PCP-based SNARKs is that the cryptographic assumptions they rely on are pretty-well understood, and are almost standard today.