Over the past half century, numerous research space missions have been launched to explore various objects in the Solar system, primarily to find surface or subsurface water or water ice (in particular, to discover extraterrestrial oceans or their traces and to study their evolution in the light of Earth's hydrospheric history). This paper briefly reviews the subject with an emphasis on the terrestrial planets to find out why is it that while liquid water oceans once formed and still exist on the Earth, the surfaces of other planets turned into arid deserts. Also reviewed are issues related to the origin and observation of water ice in the outer part of the Solar system. A list of important problems related to the origin and distribution of water in the Solar system is presented.