The construction of the $\Phi^4_3$ quantum field theory model. This was done in the early seventies by Glimm-Jaffe, Feldman, Feldman-Osterwalder, Magnen-Seneor.

This model is related to current research since it should provide the invariant measure for the stochastic quantization SPDE in three spatial dimensions (see e.g the work of Hairer, Catellier-Chouk and Kupiainen).