Flows in manifolds are of great importance in quite diverse fields of science and technology, including fuel cells, spargers, solar collectors, microchannels, porous infiltration and irrigation. Theory of flow distribution and pressure drop is vital to predict process performance and efficiency of manifold systems. In this paper, we examined research and development of theoretical models and methodology of solutions in flow in manifolds and highlight remarkable advances in the past fifty years. The main existing models and solution methods were unified further to one theoretical framework, including Bernoulli theory and momentum theory, and discrete and continuum methodologies. The generalised model was applicable to not only designs of continuum manifolds but also those of discrete manifolds with constant or varying factors. The procedure of design calculation is in reality straightforward without requirements of iteration, successive approximation and computer programme. The theoretical model provides easy-to-use design guidance to investigate the interactions among structures, operating conditions and manufacturing tolerance under a wide variety of combination of flow conditions and geometries through three general characteristic parameters (E, M and ζ) and to minimize the impact on manifold operability.