Three-loop master integrals for H+jet production at N${}^3$LO: Towards the non-planar topologies

We discuss the recent progress that has been made towards the computation of three-loop non-planar master integrals relevant to next-to-next-to-next-to-leading-order (N${}^3$LO) corrections to processes such as H+jet production at the LHC. We describe the analytic structure of these integrals, as well as several technical issues regarding their analytic computation using canonical differential equations. Finally, we comment on the remaining steps towards the computation of all relevant three-loop topologies and their application to amplitude calculations.