Since July 2014, the ESA Gaia mission has been surveying the entire sky down to magnitude 20.7 in the visible. In addition to the millions of stars, thousands of Solar System Objects (SSOs) are observed daily. By comparing their positions to those of known objects, a daily processing pipeline filters known objects from potential discoveries. However, owing to Gaia's specific scanning law designed for stars, potential newly discovered moving objects are characterized by very few observations, acquired over a limited time. This aspect was recognized early in the design of the Gaia data processing. A daily processing pipeline dedicated to these candidate discoveries was set up to release calls for observations to a network of ground-based telescopes. Their aim is to acquire follow-up astrometry and to characterize these objects. From the astrometry measured by Gaia, preliminary orbital solutions are determined, allowing to predict the position of these potentially new discovered objects in the sky accounting for the large parallax between Gaia and the Earth (separated by 0.01 au). A specific task within the Gaia Consortium has been responsible for the distribution of requests for follow-up observations of potential Gaia SSO discoveries. Since late 2016, these calls for observations (called alerts) are published daily via a Web interface, freely available to anyone world-wide. Between November 2016 and July 2020, over 1700 alerts have been published, leading to the successful recovery of more than 200 objects. Among those, six have provisional designation assigned with the Gaia observations, the others being previously known objects with poorly characterized orbits, precluding identification at the time of Gaia observations. There is a clear trend for objects with a high inclination to be unidentified, revealing a clear bias in the current census of SSOs against high inclination populations.