In general terms, my research focus is on field theoretical systems and topics related to quantum gravity. The systems include and resemble the strong coupling limit of Einstein gravity. Full Einstein gravity can be mapped into its strong coupling limit by means of a trivializing map. In terms of it several key topics are explored: First, the asymptotic safety property on which a non-perturbative notion of renormalizability can be based, overcoming the long-known perturbative non-renormalizability. Second, state space positivity which is beyond the scope of functional renormalization group techniques. Third, a gravity specific form of spontaneous symmetry breaking rooted in the impossibility to perform non-boring group averages over remnants of the diffeomorphism group after gauge fixing.