The use of fluorescence in deep-tissue imaging is rapidly expanding in last several years. The progress in fluorescent molecular probes and fluorescent imaging techniques gives an opportunity to detect single cells and even molecular targets in live organisms. The highly sensitive and high-speed fluorescent molecular sensors and detection devices allow the application of fluorescence in functional imaging. With the development of novel bright fluorophores based on nanotechnologies and 3D fluorescence scanners with high spatial and temporal resolution, the fluorescent imaging has a potential to become an alternative of the other non-invasive imaging techniques as magnetic resonance imaging, positron-emission tomography, X-ray, computing tomography. The fluorescent imaging has also a potential to give a real map of human anatomy and physiology. The current review outlines the advantages of fluorescent nanoparticles over conventional organic dyes in deep-tissue imaging in vivo and defines the major requirements to the "perfect fluorophore". The analysis proceeds from the basic principles of fluorescence and major characteristics of fluorophores, light-tissue interactions, and major limitations of fluorescent deep-tissue imaging. The article is addressed to a broad readership - from specialists in this field to university students.