A denoising algorithm seeks to remove perturbations or errors from a signal. The last three decades have seen extensive research devoted to this arena, and as a result, today's denoisers are highly optimized algorithms that effectively remove large amounts of additive white Gaussian noise. A compressive sensing (CS) reconstruction algorithm seeks to recover a structured signal acquired using a small number of randomized measurements. Typical CS reconstruction algorithms can be cast as iteratively estimating a signal from a perturbed observation. This thesis answers a natural question: How can one effectively employ a generic denoiser in a CS reconstruction algorithm? In response, in this thesis, I propose a denoising-based approximate message passing (D-AMP) algorithm that is capable of high-performance reconstruction. I demonstrate that, when used with a high performance denoiser, D-AMP offers state-of-the-art CS recovery performance for natural images while operating tens of times faster than the only competitive method. In addition, I explain the exceptional performance of D-AMP by analyzing some of its theoretical features. A critical insight into this approach is the use of an appropriate Onsager correction term in the D-AMP iterations, which coerces the signal perturbation at each iteration to be distributed approximately like the white Gaussian noise that denoisers are typically designed to remove. In doing so, this feature enables the algorithm to effectively use nearly any denoiser.