Quasi equilibrium grain structures and grain growth processes have been investigated in ordered columnar polycrystals, containing three types of grain based on tessellations of regular hexagonal or square unit cells. In particular, the families of structures containing central, vertex, and edge grains, all meeting at three fold grain edge nodes, have been examined in detail. It has been found convenient and instructive to present the principal results of this analysis on ternary diagrams of grain areas. Four regions representing topologically distinct trimodular structures arise within these diagrams, and the boundaries and corners correspond to degenerate bimocular and unimodular structures respectively. A study has been made of the equilibrium shapes adopted by pores on the boundaries of columnar grain structures. Grain growth within porous columnar polycrystals has also been examined. A model was developed to determine the velocity with which pores will move by surface diffusion while remaining attached to a grain boundary migrating during grain growth. Such pores may more readily be removed from a polycrystal by sintering than those which break away from a boundary and become isolated within a grain. The retardation in boundary migration resulting from the presence of pores is examined in specific grain configurations. It was found that when pores were small or occupied only a small fraction of a grain boundary trans-boundary migration of atoms governed growth. However, when this situation was reversed growth was increasingly dominated by surface diffusion. Similarly at high temperatures boundary migration was shown to govern growth while surface diffusion was more important at lower temperatures. The results obtained from this analysis are found to be in good agreement with the observed pattern of pore behaviour during grain growth.