Compressed sensing approach makes possible to accelerate data acquisitions. However, study for in vivo CS-fMRI or CS-CEST has not existed. in vivo CS-fMRI has some difficulties to apply CS, such as slow temporal dynamics of hemodynamic signals and concerns of statistical power loss. Also, CEST is a relatively new subject in MR imaging, so applying CS has not tried. In this study, we investigated the properties of CS-fMRI and CS-CEST by using k-t FOCUSS as a reconstruction algorithm. In the study of CS-fMRI, Functional sensitivity, specificity, and time course were used to measure the ability of CS-fMRI. Consequently, the CS-fMRI has following properties. 1) the Gaussian sampling pattern with fully sampled center one line and the random sampling pattern with 10\% low k-space lines are more sensitive than the complete random sampling pattern, 2) CS-fMRI with GRE improves the functional sensitivity and specificity over the fully sampled data, 3) CS-fMRI improves temporal resolution, and reduces temporal noises, 5) CS-fMRI is effective for both block-design and event-related paradigms in BOLD and cerebral blood volume-weighted contrasts. We conclude that CS-fMRI is a valuable tool especially for conventional GRE fMRI studies. In the study of CS-CEST, the validity of constructing z-spctrum from CS data was shown. As a result, the reconstruction of baseline images and z-spectrum is realizable from CS-CEST, albeit further work is required to establish the advantages of CS-CEST.