Intertemporal choice involves decisions between rewards available at an earlier point in time and delayed rewards (delay discounting). Such decisions are common in everyday life, influencing outcomes from personal health decisions to broader societal and political developments. Humans typically prefer smaller-but-sooner over larger-but-later rewards, although substantial inter-individual variability exists. Extreme preferences for immediate or delayed rewards are associated with various mental disorders, ranging from addictions to anorexia nervosa. Preferences are further affected by pharmacological manipulations affecting, e.g., the dopamine system, as well as factors such as episodic future thinking, emotional cueing, or other state-dependent factors. We review individual differences with clinical significance, state-dependent modulators of intertemporal choice and highlight potential intervention targets. We then introduce methods to quantify behavior on intertemporal choice tasks. First, we highlight simple, model-agnostic methods (choice proportions, area under the empirical discounting curve, AUC). We then introduce computational approaches, such as exponential and hyperbolic discounting models, and highlight recent methodological advances that integrate discounting models with evidence accumulation frameworks such as the drift diffusion model (DDM), jointly accounting for choices and response times. These approaches allow for deeper insights into underlying cognitive mechanisms. We conclude with an outlook that highlights potential future directions and open questions in the field.