Abstract
The discovery of superconductivity in nickelate compounds has opened new avenues in the study of high-temperature superconductors. Here we provide a comprehensive overview of recent progress in the field, covering various nickelate systems, including the reduced-Ruddlesden-Popper-type infinite layer LaNiO[Formula: see text] as well as the Ruddlesden-Popper-type bilayer La[Formula: see text]Ni[Formula: see text]O[Formula: see text] and trilayer La[Formula: see text]Ni[Formula: see text]O[Formula: see text]. We begin by introducing the superconducting properties of the hole-doped LaNiO[Formula: see text] system, which marked the starting point for nickelate superconductivity. We then turn to the bilayer La[Formula: see text]Ni[Formula: see text]O[Formula: see text] system, discussing both its high-pressure and thin-film superconducting phases. This is followed by an examination of the trilayer La[Formula: see text]Ni[Formula: see text]O[Formula: see text] system and other related multilayer nickelates. Throughout the review, we highlight emerging trends, key challenges and open questions. We conclude by addressing current limitations in materials synthesis and characterization, and future directions that may help uncover the mechanisms driving superconductivity in these complex oxide systems.