To be widely adopted, 3D facial avatars need to be animated easily, realistically, and directly, from speech signals. While the best recent methods generate 3D animations that are synchronized with the input audio, they largely ignore the impact of emotions on facial expressions. Instead, their focus is on modeling the correlations between speech and facial motion, resulting in animations that are unemotional or do not match the input emotion. We observe that there are two contributing factors resulting in facial animation - the speech and the emotion. We exploit these insights in EMOTE (Expressive Model Optimized for Talking with Emotion), which generates 3D talking head avatars that maintain lip sync while enabling explicit control over the expression of emotion. Due to the absence of high-quality aligned emotional 3D face datasets with speech, EMOTE is trained from an emotional video dataset (i.e., MEAD). To achieve this, we match speech-content between generated sequences and target videos differently from emotion content. Specifically, we train EMOTE with additional supervision in the form of a lip-reading objective to preserve the speech-dependent content (spatially local and high temporal frequency), while utilizing emotion supervision on a sequence-level (spatially global and low frequency). Furthermore, we employ a content-emotion exchange mechanism in order to supervise different emotion on the same audio, while maintaining the lip motion synchronized with the speech. To employ deep perceptual losses without getting undesirable artifacts, we devise a motion prior in form of a temporal VAE. Extensive qualitative, quantitative, and perceptual evaluations demonstrate that EMOTE produces state-of-the-art speech-driven facial animations, with lip sync on par with the best methods while offering additional, high-quality emotional control.