Coarse-grained (Type A, B) Ca-Al-rich inclusions (CAIs) in carbonaceous chondrites typically are surrounded by thin mineral layers (rims) that have puzzled researchers for two decades. Quantitative reaction-diffusion models can account for the overall mineral zoning structures of rims and the major-element zoning of the ubiquitous clinopyroxene layer, suggesting that the layers formed by metasomatism. Melilite-bearing CAIs appear to have reacted with an external medium that primarily contained Mg-Si-rich vapor (with atomic Mg/≤0.66) and forsteritic olivine. Different reactant compositions in the external medium appear to have been largely responsible for producing different rim types. Various rims formed either in different local environments or at different times in an evolving system. It is suggested that layer formation occurred in a nebular setting, while silicates were being vaporized and olivine was condensing around CAIs. Steady state layer growth models do not adequately explain the presence of melilite layers or patches in some rims and consistently underestimate the spinel/clinopyroxene ratios of rims, probably because of a failure to attain complete steady state conditions as a result of changing pressure, temperature, or reactant compositions during layer growth. Roughly 3--50% of the spinel in rims can be attributed to metasomatic growth, but the remaining spinel formed by another process, possibly as a residue of partial melting during a brief vaporization event, or by preferential nucleation on the surfaces of molten CAIs. The thermal events accompanying CAI metasomatism can be constrained by modeling Mg isotope exchange that occurred between some CAIs and the external medium. Based on one well-studied CAI, it is inferred that isotopic exchange and layer formation was initiated either in a high-temperature (>1450 ¿C) heating event <10 hours in duration, or at lower temperatures (≤1450 ¿C) during cooling at a rate of ≤0.1--2 ¿C/hr.¿ 1997 American Geophysical Union