Leibniz introduced the concept of apperception in philosophical discourse. But what does this concept mean? Leibniz seems to equate apperception with reflection while attributing the former to animals but not the latter. If apperception is reflection, however, how could animals possess the one without the other? This study revisits this well-known problem in Leibniz research in two main steps. Using the methodological tool of object- and process-based analyses, it first carves a distinction between apperception and reflection in order to better define the cognitive abilities of humans and animals. This conceptual work sheds light on an animal kind of apperception, yet the unity of "animal apperception" remains problematic. Since it cannot be explained by the function underlying "human apperception", this study then explores what function might account for it.