The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015–2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14 000 deg² of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

The detection of the accelerated expansion of the Universe has been one of the major breakthroughs in modern cosmology. Several cosmological probes (Cosmic Microwave Background, Supernovae Type Ia, Baryon Acoustic Oscillations) have been studied in depth to better understand the nature of the mechanism driving this acceleration, and they are being currently pushed to their limits, obtaining remarkable constraints that allowed us to shape the standard cosmological model. In parallel to that, however, the percent precision achieved has recently revealed apparent tensions between measurements obtained from different methods. These are either indicating some unaccounted systematic effects, or are pointing toward new physics. Following the development of CMB, SNe, and BAO cosmology, it is critical to extend our selection of cosmological probes. Novel probes can be exploited to validate results, control or mitigate systematic effects, and, most importantly, to increase the accuracy and robustness of our results. This review is meant to provide a state-of-art benchmark of the latest advances in emerging “beyond-standard” cosmological probes. We present how several different methods can become a key resource for observational cosmology. In particular, we review cosmic chronometers, quasars, gamma-ray bursts, standard sirens, lensing time-delay with galaxies and clusters, cosmic voids, neutral hydrogen intensity mapping, surface brightness fluctuations, stellar ages of the oldest objects, secular redshift drift, and clustering of standard candles. The review describes the method, systematics, and results of each probe in a homogeneous way, giving the reader a clear picture of the available innovative methods that have been introduced in recent years and how to apply them. The review also discusses the potential synergies and complementarities between the various probes, exploring how they will contribute to the future of modern cosmology.