This paper is to describe principles of laser optoacoustic tomography for medical diagnostics. Two types of imaging modes are presented. The first is the tomography in transmission mode, which utilizes detection of stress transients transmitted from the laser-excited volume toward the depth through thick layers of tissue. The second is the tomography in reflection mode which utilizes detection of stress transients generated in superficial tissue layer and reflected back toward tissue surface. To distinguish the two modes, we have abbreviated them as (1) laser optoacoustic tomography in transmission mode, LOATT, and (2) time-resolved stress detection tomography of light absorption, TRSDTLA, in reflection mode where emphasis is made on high spatial resolution of images. The basis for laser optoacoustic tomography is the time-resolved detection of laser-induced transient stress waves, selectively generated in absorbing tissues of diagnostic interest. Such a technique allows one to visualize absorbed light distribution in turbid biological tissues irradiated by short laser pulses. Laser optoacoustic tomography can be used for detection of tissue pathological changes that result in either increased concentration of various tissue chromophores such as hemoglobin or in development of enhanced microcirculation in diseased tissue. Potential areas of applications are diagnosis of cancer, brain hemorrhages, arterial atherosclerotic plaques, and other diseased tissues. In addition, it can provide feedback information during medical treatments. Both LOATT and TRSDTLA utilize laser excitation of biological tissues and sensitive detection of laser-induced stress waves. Optical selectivity is based upon differences in optical properties of pathologically different tissues. Sensitivity comes from stress generation under irradiation conditions of temporal stress confinement. The use of sensitive wide-band lithium niobate acoustic transducers expands limits of laser optoacoustic tomography. The technology allows us to determine directly temperature distributions in tissues and locate tissues volumes with different absorption. To demonstrate principles of TRSDTLA, experiments were conducted in vivo with mice-model for breast cancer using specially designed front-surface transducers- reflectometers. To present advantages and limitation of LOATT, experiments were performed in phantoms made of gel with polystyrene spheres colored with copper sulfate. Our experimental results and theoretical calculations show that TRSDTLA can be applied for non- invasive histology of layered tissues with in-depth resolution of up to 2 microns. TRSDTLA in acoustic reflection mode is promising for diagnostics of skin and ocular diseases. LOATT in acoustic transmission mode can be applied for detection of small tissue volumes with enhanced absorption located inside organs at the depth of up to 10 cm.