  We present a survey of rigourous quantization results obtained in recent
works on quantum free fields in de Sitter space. For the "massive'' cases which
are associated to principal series representations of the de Sitter group
SO\_0(1,4), the construction is based on analyticity requirements on the
Wightman two-point function. For the "massless'' cases (e.g. minimally coupled
or conformal), associated to the discrete series, the quantization schemes are
of the Gupta-Bleuler-Krein type.
