Issues in ATR Theory emerge by considering three levels of the ATR problem. The term "monolithic architecture (MA)-ATR" is used for problems of standard classification theory. The MA-ATR level has seen recent unification of theories that should be aggressively applied. Modern ATR systems include standard classification theoretic subsystems (e.g., feature extraction, matching, and discrimination); however they also add modeling within a search paradigm. These "aggregate architecture (AA)-ATRs" allow more direct inclusion of application-specific prior (non-sample) knowledge. Greater theoretical support is needed for analyzing AA-ATRs at the system level and integrating the strong MA-ATR theories. The third level of the ATR problem returns to the MA-ATR problem and below. The strongest elements of the MA-ATR theories deal with the stochastic aspects of the ATR problem. Structural aspects of ATRs are an important weak link in the MA-ATR theories. Function decomposition provides an "atom" towards a structural theory. Decomposition provides robustness by constructing the MA-ATR's structure from samples, but is intractable. Standard MA-ATR design is tractable, but is brittle because of an ad hoc structure selection. The key issue in either case is to make explicit use of non-sample (typically structural) knowledge in selecting or, better yet, constructing the MA-ATR's structure.