The Approximate Number System (ANS) enables organisms to represent number quickly and independently of language. It emerges early in human life and has been observed in various animal species. Despite its importance, a fundamental question remains: how are ANS representations derived from visual input? One promising approach to uncovering the underlying processes that form ANS representations is to understand when and how our perceived number is systematically distorted by stimulus features or 'tricked' by illusions. This dissertation investigates when and how the coherence illusion—where decreasing visual coherence systematically reduces perceived numerosity—emerges during visual number processing. Study 1 demonstrates the generality of the coherence effect: that the coherence effect is not limited to a specific visual property (orientation) but instead extends to other visual properties (color). Moreover, Study 1 demonstrates that the coherence effect is present in children as young as five and intensifies into adulthood. Study 2 employs a drift diffusion model to determine which components of the numerical decision processes are influenced by coherence and how this influence changes over development. I found that the coherence effect was localized to the drift rate and did not influence response bias or boundary separation, demonstrating that coherence distorts numerical calculation through biased accumulation of numerical evidence. This calculation bias increases with age as quantitative information is accumulated more efficiently over development. Study 3 examines when in the visual processing hierarchy coherence affects numerosity perception. I tested adults in an ordinal numerical comparison task and mathematically manipulated contextual coherence using a statistical model of visual object co-occurrence. I demonstrated that the coherence effect emerges via low level visual processing stages that are independent of categorical or semantic information. Study 4 introduces and tests a mechanistic model of numerosity perception—the noisy template matching model—which explains the coherence illusion while simultaneously predicting the signatures of the ANS. Together, these findings elucidate how visual information is transformed into ANS representations, providing insights into the broader mechanisms that allow us to efficiently code and simplify the complexities of the visual environment.