Abstract: Gravitational-wave (GW) cosmology has recently been established as a new observationally-driven research field, and is expected to expand rapidly in the future thanks to the increasing number of ever more accurate GW observations. In this talk I will review the current status of GW cosmological results and will survey the expectations for the future. I will first introduce the concept of "standard siren” reviewing its theoretical foundations and phenomenological applications. Standard sirens represent the most common methodology employed to extract cosmological information from GW data, including new tests of LCDM which cannot be performed with standard electromagnetic observations. I will then show how these methods are employed to produce cosmological constraints with current GW data collected by LIGO and Virgo, and how they will usher an era of precise GW cosmology with next generation GW observatories, such as the Einstein Telescope on the Earth and LISA in space.