Neuro-Symbolic (NeSy) predictive models hold the promise of improved compliance with given constraints, systematic generalization, and interpretability, as they allow to infer labels that are consistent with some prior knowledge by reasoning over high-level concepts extracted from sub-symbolic inputs. It was recently shown that NeSy predictors are affected by reasoning shortcuts: they can attain high accuracy but by leveraging concepts with \textit{unintended semantics}, thus coming short of their promised advantages. Yet, a systematic characterization of reasoning shortcuts and of potential mitigation strategies is missing. This work fills this gap by characterizing them as unintended optima of the learning objective and identifying four key conditions behind their occurrence. Based on this, we derive several natural mitigation strategies, and analyze their efficacy both theoretically and empirically. Our analysis shows reasoning shortcuts are difficult to deal with, casting doubts on the trustworthiness and interpretability of existing NeSy solutions.