A heat exchanger is constructed from a heat -conductive metal foil wound backwards and forwards in sinuous fashion to provide a stack of parallel pockets (1) between neighboring sections (8) of the foil. The pockets (1) contain baffles (5,6) which guide fluid flowing through the pockets to follow a serpentine path of U, S or M shape. The serpentine path in all the pockets is substantially the same shape but the direction of fluid flow (13) in alternate pockets is opposite to the flow direction (14) in the remaining pockets. Two corner regions of the pocket stack are each provided with two manifolds (15,16) one of which communicates with the alternate pockets (1) and the other manifold communicates with the remaining pockets (16). The pockets may be formed from a single foil or from two or more foils. The manifolds may be arranged on diagonally opposite, or on adjacent corner regions of the stack.