This paper focuses on the compressed sensing of block-sparse signals, which are signals where nonzero coefficients occur in clusters. The authors introduce a block-coherence measure to characterize the uncertainty relations for block-sparse signals. They show that a block-version of the orthogonal matching pursuit (BOMP) 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 can also guarantee successful recovery under the same condition on block-coherence. This work complements previous results that relied on small block-restricted isometry constants and demonstrates that explicitly exploiting block-sparsity can lead to better reconstruction properties compared to treating the signal as conventional sparse. The significance of the results lies in their ability to improve reconstruction accuracy by leveraging the additional structure in block-sparse signals.This paper focuses on the compressed sensing of block-sparse signals, which are signals where nonzero coefficients occur in clusters. The authors introduce a block-coherence measure to characterize the uncertainty relations for block-sparse signals. They show that a block-version of the orthogonal matching pursuit (BOMP) 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 can also guarantee successful recovery under the same condition on block-coherence. This work complements previous results that relied on small block-restricted isometry constants and demonstrates that explicitly exploiting block-sparsity can lead to better reconstruction properties compared to treating the signal as conventional sparse. The significance of the results lies in their ability to improve reconstruction accuracy by leveraging the additional structure in block-sparse signals.