The folklore knowledge is that Quantum Field Theory is (or should be) better behaved on de Sitter space than on its much better known cousin Minkowski space. The main reason are better infrared properties, which also imply better behaviour of classical non-linear fields. On top of that, de Sitter space has a remarkable asymptotic structure which underpins dS/CFT duality and survives under rather dramatic perturbations of the metric. This talk is intended as an introduction to asymptotically de Sitter spaces and as a survey of recent developments in QFT in this setting, with a special emphasis on propagators and their analytic properties.