This paper presents a framework for robust and efficient recovery of signals from a structured union of subspaces. The key idea is to model the signal as a block-sparse vector, where non-zero elements appear in fixed blocks. The authors propose a mixed $\ell_{2}/\ell_{1}$ program for block sparse recovery and derive an equivalence condition under which the proposed convex algorithm guarantees exact recovery of the original signal. This result is based on the block restricted isometry property (RIP), a generalization of the standard RIP used in compressed sensing. The block RIP ensures that the measurement matrix satisfies certain conditions that allow for stable and robust recovery in the presence of noise and modeling errors. The paper also discusses a special case of the framework, namely the recovery of multiple measurement vectors (MMV) that share a joint sparsity pattern. The authors show that their method can be adapted to this context and derive new MMV recovery methods along with equivalence conditions for efficient recovery. The results are validated through theoretical analysis and numerical examples, demonstrating the effectiveness of the proposed framework for recovering signals from a structured union of subspaces.This paper presents a framework for robust and efficient recovery of signals from a structured union of subspaces. The key idea is to model the signal as a block-sparse vector, where non-zero elements appear in fixed blocks. The authors propose a mixed $\ell_{2}/\ell_{1}$ program for block sparse recovery and derive an equivalence condition under which the proposed convex algorithm guarantees exact recovery of the original signal. This result is based on the block restricted isometry property (RIP), a generalization of the standard RIP used in compressed sensing. The block RIP ensures that the measurement matrix satisfies certain conditions that allow for stable and robust recovery in the presence of noise and modeling errors. The paper also discusses a special case of the framework, namely the recovery of multiple measurement vectors (MMV) that share a joint sparsity pattern. The authors show that their method can be adapted to this context and derive new MMV recovery methods along with equivalence conditions for efficient recovery. The results are validated through theoretical analysis and numerical examples, demonstrating the effectiveness of the proposed framework for recovering signals from a structured union of subspaces.