Some industrial defects are geometric and invisible to a color camera, and anomaly detection on point clouds, depth maps and RGB-D images grew up around them. This survey covers 2020 to 21 August 2026, 94 detectors and 17 benchmark datasets, with an executable search protocol tested against the corpus and every collated number attributed to its source. Methods sit on two axes: six mutually exclusive scoring mechanisms (feature and memory matching, reconstruction, teacher–student discrepancy, density estimation, registration, and foundation-model transfer) and eight separable design dimensions, so fusion and zero-shot supervision are properties, not families. Benchmark results are collated with protocol, metric variant and peer-review status rather than ranked: on MVTec 3D-AD, the highest image-level area under the receiver operating characteristic curve (I-AUROC) is 98.4% peer-reviewed and 97.2% in a preprint, under differing protocols; the five highest span 1.1 points. Color-and-geometry fusion leads where both are captured; density estimation and reconstruction lead on point-cloud-only, few-shot Real3D-AD. Few of the 108 works examined report enough of the fields a runtime comparison needs. Sensing robustness is mostly tested along conditions an ablation already varies, rarely along those an instrument would introduce. A closing guide states what the evidence lets a practitioner select.