In recent years， deep learning networks for point clouds have achieved remarkable advancements， with their robust semantic understanding capabilities propelling research across the entire field of three-dimensional （3D） computer vision. These advancements have enabled accurate and efficient processing of 3D data， supporting applications in autonomous driving， robotics， remote sensing and mapping， and augmented reality. However， 3D point clouds often exhibit complex transformation symmetries， with rotation being a particularly challenging yet critical factor. The spatial coordinates of point clouds， which are the fundamental input to point cloud networks， undergo substantial changes， resulting in feature output variations. However， the semantic information embedded within point clouds theoretically remains consistent under various rotational transformations. This spatial variability substantially impacts the stability and reliability of conventional point cloud deep learning networks in semantic perception tasks， such as recognition， classification， and segmentation， reducing their effectiveness in real-world scenarios characterized by arbitrary orientations and poses. Early studies primarily relied on rotational data augmentation to enhance the robustness of point cloud networks against rotational variations. While data augmentation can improve generalization to some extent， it falls short of addressing the fundamental issue posed by the infinite and continuous nature of the rotation group. Acknowledging these limitations， an increasing number of researchers have shifted their focus toward designing rotation-invariant point cloud deep learning networks， which aim to mitigate the impact of rotation on feature extraction at the architectural level. Therefore， researchers seek to achieve consistent semantic perception regardless of point cloud orientation， thereby enhancing the applicability of deep learning models in real-world scenarios where data can be encountered in arbitrary poses. This paper presents a comprehensive survey of the current state of research on rotation-invariant point cloud networks. The research background is first outlined to highlight the importance of rotation invariance in 3D vision tasks and the challenges posed by rotational symmetries in point cloud data. Then， a systematic categorization of the prevailing mainstream methods is investigated. Particularly， the rotation-invariant point cloud networks can be broadly classified into the following three categories： 1） geometric-guided rotation-invariant methods： Using the traditional geometric analysis algorithms， these methods extract rotation-invariant geometric representations such as relative distances， angles， local reference frames， and canonical poses. These representations are then integrated into point cloud networks， facilitating learning of high-level semantic features and maintaining robustness to rotational transformations simultaneously. 2） Feature-guided rotation-invariant methods： These methods employ rotation-equivariant point cloud networks to extract point cloud representations that contain shape and pose information. Leveraging the inherent principles of equivariant networks， they subsequently remove the pose information from the rotation-equivariant representations， obtaining rotation-invariant point cloud features. 3） Training-guided rotation-invariant methods： These methods focus on designing sophisticated and highly generalizable rotational data augmentation training schemes， allowing non-rotation-invariant point cloud networks to gradually acquire robustness of rotations and achieve stable performance simultaneously. An in-depth analysis of the core concepts and algorithmic improvements that support these methods is provided for each category. The current research content on this issue and methodologies within the academic community are outlined， and the advantages and disadvantages of each method are summarized and compared. Subsequently， a comprehensive overview of the prevalent downstream tasks in the research of rotation-invariant point cloud networks is presented. These tasks include point cloud classification， point cloud segmentation， and point cloud retrieval. For each of these tasks， an in-depth discussion of the commonly employed datasets and evaluation metrics， which are essential for assessing network performance， is provided. Additionally， the quantitative performance metrics of mainstream rotation-invariant point cloud networks applied to these tasks are summarized and analyzed， offering a comparative perspective on their efficacy and robustness under rotational variations. Afterward， the downstream application prospects of rotation-invariant point cloud deep learning networks， including point cloud self-supervised representation learning， end-to-end point cloud registration， and point cloud completion， are examined and summarized. Finally， an outlook on future developments and research hotspots is presented. In addition to the ongoing development of new rotation-invariant point cloud networks， three primary issues warrant further research： 1） discrimination of effective geometric attributes. Current approaches are limited by the design of geometric attribute extraction algorithms. An in-depth discussion and determination of the effectiveness of different rotation-invariant geometric attributes within deep learning frameworks could yield novel insights and foster the development of innovative strategies to advance this field. 2） Highly integratable rotation-invariant mechanism. On the one hand， existing non-rotation-invariant point cloud networks continue to demonstrate strong performance on aligned data. The challenge lies in incorporating rotation invariance into these networks in a straightforward manner degrading their original performance. This challenge remains a key research topic because seamless integration requires innovative architectural designs and methodological approaches. On the other hand， rotation-invariant point cloud networks should also exhibit simplicity and reusability， enabling their direct application to downstream tasks with minimal adaptation. 3） High computational efficiency in invariant feature extraction modules. Although many existing methods demonstrate commendable performance， they often incur substantial time and computational costs， making it challenging to efficiently process large-scale point cloud data. Therefore， designing more efficient rotation-invariant point cloud networks that maintain robust feature extraction capabilities while minimizing computational overhead is crucial. Addressing the aforementioned challenges will notably enhance the effectiveness and practicality of rotation-invariant point cloud deep learning networks， facilitating their widespread adoption in complex 3D environments. This survey aims to provide researchers in 3D computer vision with a foundational understanding of current methodologies， highlight key challenges， and suggest potential avenues for future research.