Framing effects in individual decision-making have puzzled economists for decades because they are hard, if at all, to explain with rational choice theories. Why should mere changes in the description of a choice problem affect decision-making? Here, we examine the hypothesis that changes in framing cause changes in the allocation of attention to the different options – measured via eye-tracking – and give rise to changes in decision-making. We document that the framing of a sure alternative as a gain – as opposed to a loss – in a risk-taking task increases the attentional advantage of the sure option and induces a higher choice frequency of that option – a finding that is predicted by the attentional drift-diffusion model (aDDM). The model also correctly predicts other key findings such as that the increased attentional advantage of the sure option in the gain frame should also lead quicker decisions in this frame. In addition, the data reveal that increasing risk aversion at higher stake sizes may also be driven by attentional processes because the sure option receives significantly more attention – regardless of frame – at higher stakes. We also corroborate the causal impact of framing-induced changes of attention on choice with an additional experiment that manipulates attention exogenously. Finally, to study the precise mechanisms underlying the framing effect we structurally estimate an aDDM that allows for frame and option-dependent parameters. The estimation results indicate that – in addition to the direct effects of framing-induced changes in attention on choice – the gain frame also causes (i) an increase in the attentional discount of the gamble and (ii) an increased concavity of utility. Our findings suggest that the traditional explanation of framing effects in risky choice in terms of a more concave value function in the gain domain is seriously incomplete and that attentional mechanisms as hypothesized in the aDDM play a key role.