Stereoscopic imagery often aims to evoke three-dimensional (3-D) percepts that are accurate and realistic-looking. The "gap" between 3-D imagery and real scenes is small, but focus cues typically remain incorrect because images are displayed on a single focal plane. Research has concentrated on the resulting vergence-accommodation conflicts. Yet, incorrect focus cues may also affect the appearance of 3-D imagery. We investigated whether incorrect focus cues reduce perceived realism of 3-D structure ("depth realism"). Experiment 1 used a multiple-focal-planes display to compare depth realism with correct focus cues vs. conventional stereo presentation. The stimuli were random-dot stereograms, which isolated the role of focus cues. Depth realism was consistently lower with incorrect focus cues, providing proof-of-principle evidence that they contribute to perceptual realism. Experiments 2 and 3 examined whether focus cues play a similar role with realistic objects, presented with an almost complete set of visual cues using a high-resolution, high-dynamic-range multiple-focal-planes display. We also examined the efficacy of approximating correct focus cues via gaze-contingent depth-of-field rendering. Improvements in depth realism with correct focus cues were less clear in more realistic scenes, indicating that the role of focus cues in depth realism depends on scene content. Rendering-based approaches, if anything, reduced depth realism, which we attribute to their inability to present higher-order aspects of blur correctly. Our findings suggest future general 3-D display solutions may need to present focus cues correctly to maximise perceptual realism.