This paper addresses the problem of recovering a signal \( x \) that lies in a union of subspaces from a set of samples. The authors develop a general framework for robust and efficient recovery, focusing on the case where \( x \) lies in a sum of \( k \) subspaces chosen from a larger set of \( m \) possibilities. The samples are modeled as inner products with an arbitrary set of sampling functions. To derive an efficient and robust recovery algorithm, the problem is formulated as that of recovering a block-sparse vector whose non-zero elements appear in fixed blocks. A mixed \( \ell_2/\ell_1 \) program is proposed for block-sparse recovery. The main result is an equivalence condition under which the proposed convex algorithm is guaranteed to recover the original signal. This result relies on the concept of block restricted isometry property (RIP), which generalizes the standard RIP used in compressed sensing. The authors also prove stability of the approach in the presence of noise and modeling errors. A special case of the framework is the multiple measurement vectors (MMV) problem, where the goal is to recover multiple measurement vectors that share a joint sparsity pattern. The paper provides new MMV recovery methods and equivalence conditions under which the entire set can be determined efficiently.This paper addresses the problem of recovering a signal \( x \) that lies in a union of subspaces from a set of samples. The authors develop a general framework for robust and efficient recovery, focusing on the case where \( x \) lies in a sum of \( k \) subspaces chosen from a larger set of \( m \) possibilities. The samples are modeled as inner products with an arbitrary set of sampling functions. To derive an efficient and robust recovery algorithm, the problem is formulated as that of recovering a block-sparse vector whose non-zero elements appear in fixed blocks. A mixed \( \ell_2/\ell_1 \) program is proposed for block-sparse recovery. The main result is an equivalence condition under which the proposed convex algorithm is guaranteed to recover the original signal. This result relies on the concept of block restricted isometry property (RIP), which generalizes the standard RIP used in compressed sensing. The authors also prove stability of the approach in the presence of noise and modeling errors. A special case of the framework is the multiple measurement vectors (MMV) problem, where the goal is to recover multiple measurement vectors that share a joint sparsity pattern. The paper provides new MMV recovery methods and equivalence conditions under which the entire set can be determined efficiently.