A detailed, systematic petrographic survey of all (189) Ca, Al-rich and olivine-rich inclusions larger than ~0.2 mm in diameter in 17 thin sections of Allende was performed by optical and scanning electron microscopy. Most of these inclusions are aggregates containing varying proportions of three distinct constituents, termed concentric objects, chaotic material, and inclusion matrix. A new classification system for Allende inclusions is proposed. Olivine-rich inclusions occur in two textural varieties: unrimmed olivine aggregates (Type 1A inclusions) and rimmed olivine aggregates (Type 1B inclusions). We classify Ca, Al-rich inclusions (CAI's) on the basis of the size and abundance of their constituent concentric objects (rather than their grain size) into unrimmed complex CAI's (Type 2 inclusions), rimmed complex CAI's (Type 3 inclusions), and simple CAI's (Type 4 inclusions). Several of the inclusion classes grade into each other. Some fundamental relationships among various types of Allende inclusions are discussed. We suggest that the term 'coarse-grained', even if used only in a relative sense, is too restrictive for some members of one class of inclusion (simple CAI's) and is inappropriate for most members of another class (melilite-rich complex CAI's).