A comprehensive theoretical investigation on the field-driven reorientation transitions in uniaxial multilayers with antiferromagnetic coupling is presented. It is based on a complete survey of the one-dimensional solutions for the basic phenomenological (micromagnetic) model that describes the magnetic properties of finite stacks made from ferromagnetic layers coupled antiferromagnetically through spacer layers. The general structure of the phase diagrams is analysed. At a high ratio of uniaxial anisotropy to antiferromagnetic interlayer exchange, only a succession of collinear magnetic states is possible. With increasing field first-order (metamagnetic) transitions occur from the antiferromagnetic ground-state to a set of degenerate ferrimagnetic states and to the saturated ferromagnetic state. At low anisotropies, a first-order transition from the antiferromagnetic ground-state to an inhomogeneous spin-flop state occurs. Between these two regions, transitional magnetic phases occupy the range of intermediate anisotropies. Detailed and quantitative phase diagrams are given for the basic model of antiferromagnetic multilayer systems with N = 2 to 16 layers. The connection of the phase diagrams with the spin-reorientation transitions in bulk antiferromagnets is discussed. The limits of low anisotropy and large numbers of layers are analysed by two different representations of the magnetic energy, namely, in terms of finite chains of staggered vectors and in a general continuum form. It is shown that the phenomena widely described as ``surface spin-flop are driven only by the cut exchange interactions and the non-compensated magnetic moment at the surface layers of a stacked antiferromagnetic system.
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