Inattentional blindness is the psychological phenomenon that causes one to miss things in plain sight. It is a consequence of the selective attention in perception that lets us remain focused on important parts of our world without distraction from irrelevant details. Motivated by selective attention, we study the properties of artificial agents that perceive the world through the lens of a self-attention bottleneck. By constraining access to only a small fraction of the visual input, we show that their policies are directly interpretable in pixel space. We find neuroevolution ideal for training self-attention architectures for vision-based reinforcement learning (RL) tasks, allowing us to incorporate modules that can include discrete, non-differentiable operations which are useful for our agent. We argue that self-attention has similar properties as indirect encoding, in the sense that large implicit weight matrices are generated from a small number of key-query parameters, thus enabling our agent to solve challenging vision based tasks with at least 1000x fewer parameters than existing methods. Since our agent attends to only task critical visual hints, they are able to generalize to environments where task irrelevant elements are modified while conventional methods fail. Videos of our results and source code available at https://attentionagent.github.io/