The received view is that superluminal signalling is prohibited in relativistic theories and allowed in non-relativistic theories. In line with this received view, there are special circumstances under which superluminal signalling with non-selective measurements is not permitted in non-relativistic quantum mechanics (NRQM), but not a general prohibition. I will survey some examples of hybrid models that combine non-relativistic and relativistic assumptions and which permit superluminal signalling with non-selective measurements. These examples illustrate that both the relativistic dynamics and a relativistic model of local measurement operations contribute to the prohibition on superluminal signalling in relativistic quantum theories.