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Numerical competence is one of the many aspects of animal cognition that have enjoyed a resurgence of interest during the past decade. Evidence for numerical abilities in animals has followed a tortuous path to respectability, however, from Clever Hans, the counting horse, to modern experimental studies. Recent surveys of the literaturereveal theoretical as well as definitional confusion arising from inconsistent terminology for numerical processes and procedures. The term “counting” has been applied to situations having little to do with its meaning in the human literature. We propose a consistent vocabulary and theoretical framework for evaluating numerical competence. Relative numerousness judgments, subitizing, counting, and estimation may be the essential processes by which animals perform numerical discriminations. Ordinality, cardinality, and transitivity also play an important role in these processes. Our schema is applied to a variety of recent experimental situations. Some evidence of transfer is essential in demonstrating higher-order ability such as counting or “sense of number.” Those instances of numerical competence in which all viable alternatives to counting (e.g., subitizing) have been precluded, but no evidence of transfer has been demonstrated might be described as “protocounting.” To show that animals are capable of “true” counting future research will have to demonstrate generality across situations.