This thesis provides a novel model for reward-based modulation of reaction times in perceptual decisions and performs neural data analysis on extremely large-scale recordings to examine brain-wide correlations. The visual search work aims to develop a comprehensive model that explains perceptual decisions, considering reaction time distributions and the impact of changing reward on decision making. It proposes a unique drift-diffusion model with dynamic bounds influenced by reward and time and provides a way to unify two disparate approaches to the study of decision making in the brain. On the other hand, the brain-wide map project investigates the representation of multiple task variables across various brain regions using linear encoding models. A large-scale neural data analysis is conducted on mice performing a decision-making task. Key findings include the widespread sensitivity of neurons to task feedback, particularly reward delivery, as well as general signatures of movement and vigor. Together these two bodies of work provide novel insights into the neural representation of decisions and a potential model of how such decisions are made under time pressure.