Model-based compressive sensing (CS) improves upon traditional CS by incorporating realistic signal models that go beyond simple sparsity and compressibility. Traditional CS requires $ M = \mathcal{O}(K \log(N/K)) $ measurements for robust recovery of K-sparse or compressible signals. Model-based CS leverages structural dependencies between signal coefficients to reduce the number of measurements to $ M = \mathcal{O}(K) $, enabling more efficient recovery. This paper introduces a model-based CS theory that provides concrete guidelines for creating recovery algorithms with provable performance guarantees. It defines a new class of structured compressible signals and introduces the restricted amplification property (RAMP) as a counterpart to the restricted isometry property (RIP) in conventional CS. Two examples demonstrate the application of model-based CS to wavelet tree and block sparsity models, showing robust recovery from $ M = \mathcal{O}(K) $ measurements. Numerical simulations validate the theory and algorithms, demonstrating their effectiveness in compressing and recovering signals with structured sparsity or compressibility. The paper also discusses the computational complexity of model-based recovery and its robustness to model mismatch. The results show that model-based CS can significantly reduce the number of measurements required for signal recovery while maintaining robustness and accuracy.Model-based compressive sensing (CS) improves upon traditional CS by incorporating realistic signal models that go beyond simple sparsity and compressibility. Traditional CS requires $ M = \mathcal{O}(K \log(N/K)) $ measurements for robust recovery of K-sparse or compressible signals. Model-based CS leverages structural dependencies between signal coefficients to reduce the number of measurements to $ M = \mathcal{O}(K) $, enabling more efficient recovery. This paper introduces a model-based CS theory that provides concrete guidelines for creating recovery algorithms with provable performance guarantees. It defines a new class of structured compressible signals and introduces the restricted amplification property (RAMP) as a counterpart to the restricted isometry property (RIP) in conventional CS. Two examples demonstrate the application of model-based CS to wavelet tree and block sparsity models, showing robust recovery from $ M = \mathcal{O}(K) $ measurements. Numerical simulations validate the theory and algorithms, demonstrating their effectiveness in compressing and recovering signals with structured sparsity or compressibility. The paper also discusses the computational complexity of model-based recovery and its robustness to model mismatch. The results show that model-based CS can significantly reduce the number of measurements required for signal recovery while maintaining robustness and accuracy.