Highly discriminative 3D shape representations can be formed by encoding the spatial relationship among virtual words into the Bag of Words (BoW) method. To achieve this challenging task, several unresolved issues in the encoding procedure must be overcome for 3D shapes, including: 1) arbitrary mesh resolution; 2) irregular vertex topology; 3) orientation ambiguity on the 3D surface; and 4) invariance to rigid and non-rigid shape transformations. In this paper, a novel spatially enhanced 3D shape representation called bag of spatial context correlations (BoSCCs) is proposed to address all these issues. Adopting a novel local perspective, BoSCC is able to describe a 3D shape by an occurrence frequency histogram of spatial context correlation patterns, which makes BoSCC become more compact and discriminative than previous global perspective-based methods. Specifically, the spatial context correlation is proposed to simultaneously encode the geometric and spatial information of a 3D local region by the correlation among spatial contexts of vertices in that region, which effectively resolves the aforementioned issues. The spatial context of each vertex is modeled by Markov chains in a multi-scale manner, which thoroughly captures the spatial relationship by the transition probabilities of intra-virtual words and the ones of inter-virtual words. The high discriminability and compactness of BoSCC are effective for classification and retrieval, especially in the scenarios of limited samples and partial shape retrieval. Experimental results show that BoSCC outperforms the state-of-the-art spatially enhanced BoW methods in three common applications: global shape retrieval, shape classification, and partial shape retrieval.