Numerous hydrogenated molecules observed in comets and the interstellar medium present nuclear spin isomers. The non-thermal ortho: para ratios measured in space are believed to be of high diagnostic value, allowing remote measurement of physical conditions prevailing in the past, such as the initial temperature associated with a molecular formation or condensation. The lack of laboratory studies on interactions at the gas-solid interface limits our current interpretation of observations. Recent progress in nuclear spin conversion (NSC) dynamics are discussed in this paper. Results on water and methane in cryogenic matrices illustrate the conversion mechanisms within the condensed phase at very low temperatures. NSC of molecular hydrogen at the surface of 10 K Amorphous Solid Water (ASW) shows surface mediated conversion processes for molecular hydrogen. NSC involving molecular ices are discussed in the light of few recent studies, including UV photodesorption investigations.