Sheep body size parameters have been increasingly recognized as critical indicators to evaluate growth performance, linear conformation, and genetic improvement in the livestock industry. However, manual measurement relied heavily on contact tools. Severe stress responses can be induced in animals due to low efficiency and high labor intensity. Furthermore, conventional approaches cannot fully meet the high-throughput and high-precision data demands in modern intensive animal husbandry. Consequently, non-contact measurement can be expected for smart farming using computer vision. In this study, a systematic review was presented on the current research advances in the key technologies for non-contact measurement of sheep body size. Technological history was traced from the two-dimensional machine vision to the three-dimensional point cloud reconstruction, as well as the emerging multimodal fusion frameworks. Data acquisition was also analyzed under different agricultural scenarios. A systematic evaluation was performed on application matching, advantages, and technical bottlenecks of the mobile portable devices, fixed-channel systems, and fixed-arch measurement platforms. These acquisitions were examined in the context of both vast grazing pastures and intensive housing environments. Unmanned Aerial Vehicles (UAVs) were analyzed for online tracking and spatial parameter estimation in the open pastures. Deep comparative analysis was conducted on the measurement accuracy and algorithmic robustness between the linear and arc parameters. In the two-dimensional visual extraction, the relative error of the linear traits was typically controlled within a low range, while the estimation of the arc traits suffered from significant errors, due to the loss of depth information and perspective distortion. Three-dimensional point cloud approaches demonstrated superior spatial geometric representation to reduce the linear measurement error after the direct Euclidean distance calculations. Great challenges also remained in arc measurements, even with the spatial depth. The high precision was still severely limited at present, although the point cloud slicing and curve fitting algorithms, like the cubic B-spline fitting, improved the accuracy. The degradation was attributed to the self-occlusion of the sheep's abdomen and inner thighs, as well as the non-linear expansion caused by the thick wool. Moreover, the target segmentation and key-point localization were summarized from the conventional handcrafted geometric features to the data-driven deep learning models. The latest breakthroughs were also highlighted in multimodal fusion technologies. Specifically, the YOLOv12 instance segmentation and point cloud geometric fitting were combined to effectively decouple the trunk distortion and complex backgrounds. Another application was given on the partly pose normalization, which was utilized to align the irregular postures for the low nonlinear errors. Critical bottlenecks were identified in the current measurement techniques. The dynamic adaptability of the algorithms was significantly degraded under continuous motion scenarios. Severe motion blur and point cloud tearing were found in the fast-paced sorting channels. The algorithmic generalization was also hindered by the breed variations. The thick-wool breeds, such as the Tibetan sheep, suffered from severe key-point drift, compared with the short-hair breeds, resulting in the failure of the geometric feature extraction. Finally, the future trends of sheep body measurement were predicted from the single-source perception to the multi-modal data fusion. The depth cameras were integrated with thermal imaging or solid-state LiDAR under complex illumination and harsh farm environments. Lightweight neural networks and edge computing architectures were urgently required for the real-time processing deployment of the massive point clouds. The instant pose normalization and parameter calculation were realized at the edge end. Moreover, the large-scale, crossbreed, and full-lifecycle open-source phenotypic databases were also provided for standardized benchmarks. A recent dataset of three-dimensional point clouds for the Jining Qing goats can be expected to enhance the generalization of models. Modules can be integrated into the daily workflows of the sheep farms, particularly for the ultimate pathway. Highly protected sensors can be embedded into the smart feeding stations or weighing-sorting gates for imperceptible, stress-free, and high-throughput morphometric monitoring. Overall, this review can provide a strong reference for the application of key technologies in smart animal husbandry.