Recently, the steady-state process of convective assembly has emerged as a viable production route for colloidal monolayers. The present study models the regions of particle assembly: Region I comprises convective concentration of a particle suspension in a liquid below a meniscus, Region II comprises permeation of fluid through the dense particle monolayer, and Region III comprises capillary densification. For each region, the dominant physics and nondimensional groups are identified, and quantitative models are derived to describe the evolution of microstructure in terms of the main process parameters. The concentration profile within the assembly zone of Region I is predicted, including the role of a concentration-dependent diffusion constant and the shape of the meniscus. The fluid flow through the assembled monolayer is treated in Region II, along with a stability calculation to reveal that isolated particle clusters do not survive on top of the monolayer. The physics of capillary crystallization is addressed in Region III, with an emphasis on the density of cracks that emerge. The Peclet number and Capillary number both play important roles but in different regions of the assembly process.