Optoacoustics is a promising modality for biomedical imaging, sensing, and monitoring with high resolution and contrast. In this paper, we present an overview of our studies for the last two decades on optoacoustic effects in tissues and imaging capabilities of the optoacoustic technique. In our earlier optoacoustic works we studied laser ablation of tissues and tissue-like media and proposed to use optoacoustics for imaging in tissues. In mid-90s we demonstrated detection of optoacoustic signals from tissues at depths of up to several centimeters, well deeper than the optical diffusion limit. We then obtained optoacoustic images of tissues both in vitro and in vivo. In late 90s we studied optoacoustic monitoring of thermotherapy: hyperthermia, coagulation, and freezing. Then we proposed and studied optoacoustic monitoring of blood oxygenation, hemoglobin concentration, and other physiologic parameters.