This paper presents a study on the compressed sensing of block-sparse signals, focusing on the derivation of uncertainty relations and efficient recovery algorithms. Block-sparse signals are those where nonzero coefficients occur in clusters or blocks. The paper introduces a new measure called block-coherence, which quantifies the similarity between blocks in a dictionary used for signal representation. This measure is used to derive an uncertainty relation for block-sparse signals, which generalizes the sparse case. The paper also shows that a block version of the orthogonal matching pursuit (OMP) algorithm can recover block k-sparse signals in no more than k steps if the block-coherence is sufficiently small. Similarly, a mixed $\ell_{2}/\ell_{1}$-optimization approach is shown to guarantee successful recovery under the same condition. The results demonstrate that leveraging block-sparsity can lead to better reconstruction properties than treating the signal as sparse in the conventional sense. The paper also extends the OMP algorithm to the block-sparse case, termed block-OMP (BOMP), and shows that it can recover block k-sparse signals efficiently under the block-coherence condition. Theoretical analysis and numerical results are provided to support these findings. The study highlights the importance of explicitly considering block-sparsity in compressed sensing applications to achieve improved performance.This paper presents a study on the compressed sensing of block-sparse signals, focusing on the derivation of uncertainty relations and efficient recovery algorithms. Block-sparse signals are those where nonzero coefficients occur in clusters or blocks. The paper introduces a new measure called block-coherence, which quantifies the similarity between blocks in a dictionary used for signal representation. This measure is used to derive an uncertainty relation for block-sparse signals, which generalizes the sparse case. The paper also shows that a block version of the orthogonal matching pursuit (OMP) algorithm can recover block k-sparse signals in no more than k steps if the block-coherence is sufficiently small. Similarly, a mixed $\ell_{2}/\ell_{1}$-optimization approach is shown to guarantee successful recovery under the same condition. The results demonstrate that leveraging block-sparsity can lead to better reconstruction properties than treating the signal as sparse in the conventional sense. The paper also extends the OMP algorithm to the block-sparse case, termed block-OMP (BOMP), and shows that it can recover block k-sparse signals efficiently under the block-coherence condition. Theoretical analysis and numerical results are provided to support these findings. The study highlights the importance of explicitly considering block-sparsity in compressed sensing applications to achieve improved performance.