To translate synthetic aperture radar (SAR) image into interpretable forms for human understanding is the ultimate goal of SAR advanced information retrieval. Existing methods mainly focus on 3D surface reconstruction or local geometric feature extraction of targets, neglecting the role of structural modeling in capturing semantic information. This paper proposes a novel task: SAR target structure recovery, which aims to infer the components of a target and the structural relationships between its components, specifically symmetry and adjacency, from a single-view SAR image. Through learning the structural consistency and geometric diversity across the same type of targets as observed in different SAR images, it aims to derive the semantic representation of target directly from its 2D SAR image. To solve this challenging task, a two-step algorithmic framework based on structural descriptors is developed. Specifically, in the training phase, it first detects 2D keypoints from real SAR images, and then learns the mapping from these keypoints to 3D hierarchical structures using simulated data. During the testing phase, these two steps are integrated to infer the 3D structure from real SAR images. Experimental results validated the effectiveness of each step and demonstrated, for the first time, that 3D semantic structural representation of aircraft targets can be directly derived from a single-view SAR image.