Underwater optical wireless communications (UOWC) have gained a considerable interest during the last years as an alternative means for broadband inexpensive submarine communications. UOWC present numerous similarities compared to free space optical (FSO) communications or laser satellite links mainly due to the fact that they employ optical wavelengths to transfer secure information between dedicated point-to-point links. By using suitable wavelengths, high data rates can be attained. Some recent works showed that broadband links can be achieved over moderate ranges. Transmissions of several Mbps have been realized in laboratory experiments by employing a simulated aquatic medium with scattering characteristics similar to oceanic waters. It was also demonstrated that UOWC networks are feasible to operate at high data rates for medium distances up to a hundred meters. However, it is not currently available as an industrial product and mainly test-bed measurements in water test tanks have been reported so far. Therefore, extensive research is expected in the near future, which is necessary in order to further reveal the "hidden" abilities of optical spectrum to transfer broadband signals at higher distances. The present work summarizes the recent advances in channel modeling and system analysis and design in the area of UOWC.