A pipe-in-pipe assembly comprises thermally-insulating spacers (24) positioned in an annulus (16) to act radially between inner and outer pipes (12, 18). The spacers comprise at least one circumferentially-extending array of circumferentially-spaced ribs (26) that define longitudinally-extending passageways in gaps (28) between neighbouring ribs of the array. Cables (10) including heating elements extend longitudinally along the annulus outside the inner pipe. The cables extend longitudinally along the passageways. At least one insulation layer (48, 52) disposed radially outboard of the cables comprises insulating elements disposed in the gaps between the ribs and/or an insulating layer extending around the inner pipe, positioned radially outboard of the ribs and bridging the gaps. Bands encircle and retain components of the insulation layer. Insulation may also be disposed on the inner pipe between first and second arrays of ribs, those arrays being spaced longitudinally from each other.