This paper presents a review of the current knowledge on the doubly-charged atomic and molecular positive ions in the planetary atmospheres of the Solar System. It is focused on the terrestrial planets which have a dense atmosphere of N(2) or CO(2), i.e. Venus, the Earth and Mars, but also includes Titan, the largest satellite of Saturn, which has a dense atmosphere composed mainly of N(2) and a few percent of methane. Given the composition of these neutral atmospheres, the following species are considered: C(++), N(++), O(++), CH(4)(++), CO(++), N(2)(++), NO(++), O(2)(++), Ar(++) and CO(2)(++). We first discuss the status of their detection in the atmospheres of planets. Then, we provide a comprehensive review of their complex and original photochemistry, production and loss processes. Synthesis tables are provided for those ions, while a discussion on individual species is also provided. Methods for detecting doubly-charged ions in planetary atmospheres are presented, namely with mass-spectrometry, remote sensing and fine plasma density measurements. A section covers some original applications, like the possible effect of the presence of doubly-charged ions on the escape of an atmosphere, which is a key topic of ongoing planetary exploration, related to the evolution of a planet. The results of models, displayed in a comparative way for Venus, Earth, Mars and Titan, are discussed, as they can predict the presence of doubly-charged ions and will certainly trigger new investigations. Finally we give our view concerning next steps, challenges and needs for future studies, hoping that new scientific results will be achieved in the coming years and feed the necessary interdisciplinary exchanges amongst different scientific communities.