Tissue perfusion is an important indicator of the health and vitality of organs such as liver and kidney. Imaging tissue perfusion has significant clinical applications such as myocardial infarction. Contrast-enhanced ultrasound (CEUS) has been clinically used in imaging myocardial perfusion since the 1990s. It was realized, however, that standard B-mode imaging did not have the specificity required to image tissue perfusion in other clinical applications, e.g. tumor perfusion. Microbubble ultrasound contrast agents (UCA) composed of an elastic shell and inert gas content are able to generate nonlinear harmonics. Therefore, nonlinear methods such as harmonic, subharmonic and multipulse imaging were proposed to improve the sensitivity and specificity of perfusion imaging. In this dissertation, a novel method to image the nonlinear response of UCA is investigated by extracting the signal using an adaptive third-order Volterra filter (TVF). Unlike harmonic and sub-harmonic imaging methods, the TVF separates the linear, quadratic and cubic components from the beamformed pulse-echo data to capture polynomial nonlinearities throughout the system bandwidth. This allows for imaging using broadband pulse transmission to preserve the axial resolution and the signal to noise ratio (SNR). In addition, the quadratic and cubic kernels of the TVF inherently suppress additive Gaussian noise, which lowers the noise floor and improves the detection of UCA activity in low-perfusion regions. Results from in vitro and in vivo imaging experiments have demonstrated the significance of the advantage of the post-beamforming VF in imaging UCA activity. Under microflow conditions (as in blood microcirculation), the echogenicity of the UCA microbubbles exhibit temporal dynamics different from the surrounding tissue. For example, the temporal variance of the echogenicity in the presence of UCA is typically higher than that of the same tissue in the absence of UCA. We introduced the temporal perfusion index (TPI) to capture UCA dynamic activity under microflow conditions. The TPI is a spatial measurement that rewards temporal variance at a given image pixel and penalizes the average image intensity over a small spatial mask. An appropriate selection of dynamic range reduces the sensitivity of the TPI to noise and improves the specificity to temporal contrast variations. This approach for finding the "threshold dynamic range" is extended to account for the breathing motion when the method is applied to in vivo data. The VF and TPI methods were applied to a variety of data sets collected from in vitro and in vivo imaging targets. These include micro channels embedded in tissue-mimicking phantoms, subcutaneous tumors in vivo and brain tissue in vivo with and without UCA. The results clearly demonstrate the advantages of the proposed methods in imaging UCA activity under microflow conditions and show the way towards quantitative noninvasive perfusion imaging using pulse-echo ultrasound.