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We introduce an Attention Overload Model that captures the idea that alternatives compete for the decision maker's attention, and hence the attention that each alternative receives decreases as the choice problem becomes larger. We provide testable implications on the observed choice behavior that can be used to (point or partially) identify the decision maker's preference and attention frequency. We then enhance our attention overload model to accommodate heterogeneous preferences based on the idea of List-based Attention Overload, where alternatives are presented to the decision makers as a list that correlates with both heterogeneous preferences and random attention. We show that preference and attention frequencies are (point or partially) identifiable under nonparametric assumptions on the list and attention formation mechanisms, even when the true underlying list is unknown to the researcher. Building on our identification results, we develop econometric methods for estimation and inference.