The precise characterization of plant morphology provides valuable insights into plant environment interactions and genetic evolution. A key technology for extracting this information is 3D segmentation, which delineates individual plant organs from complex point clouds. Despite significant progress in general 3D computer vision domains, the adoption of 3D segmentation for plant phenotyping remains limited by three major challenges: i) the scarcity of large-scale annotated datasets, ii) technical difficulties in adapting advanced deep neural networks to plant point clouds, and iii) the lack of standardized benchmarks and evaluation protocols tailored to plant science. This review systematically addresses these barriers by: i) providing an overview of existing 3D plant datasets in the context of general 3D segmentation domains, ii) systematically summarizing deep learning-based methods for point cloud semantic and instance segmentation, iii) introducing Plant Segmentation Studio (PSS), an open-source framework for reproducible benchmarking, and iv) conducting extensive quantitative experiments to evaluate representative networks and sim-to-real learning strategies. Our findings highlight the efficacy of sparse convolutional backbones and transformer-based instance segmentation, while also emphasizing the complementary role of modeling-based and augmentation-based synthetic data generation for sim-to-real learning in reducing annotation demands. In general, this study bridges the gap between algorithmic advances and practical deployment, providing immediate tools for researchers and a roadmap for developing data-efficient and generalizable deep learning solutions in 3D plant phenotyping. Data and code are available at https://github.com/perrydoremi/PlantSegStudio.