A new form of liquid matter: quantum droplets Quantum droplets (QDs) are robust two- and three-dimensional self-trapped states in Bose-Einstein condensates (BECs), stabilized by effective self-repulsion induced by quantum fluctuations around the mean-field (MF) states, known as the Lee-Huang-Yang (LHY) effect. This review summarizes recent theoretical and experimental results on QDs, focusing on their existence in binary and single-component BECs, and their stability with embedded vorticity. Theoretical models of QDs in three, two, and one dimensions are discussed, along with dimensional crossover from 3D to 2D and 1D. Experimental observations include stable 3D and quasi-2D QDs in binary BECs, and single-component QDs in dipolar condensates. Theoretical results highlight the stability of QDs with embedded vorticity, such as three-dimensional vortex rings and two-dimensional vortex rings and necklaces. Additionally, the review addresses the behavior of QDs in singular potentials and their stability against collapse due to the LHY effect. The review also discusses the creation of QDs in heteronuclear bosonic mixtures and their long lifetimes, which allow for the observation of intrinsic properties like self-evaporation. In single-component dipolar BECs, QDs are stabilized by long-range dipole-dipole interactions and contact interactions, including the LHY term. The review highlights the experimental realization of QDs in dysprosium and erbium atoms, demonstrating their stability and the emergence of interference fringes, indicating phase coherence. Theoretical and experimental findings confirm the possibility of creating stable QDs in binary BECs through the competition between cubic attraction and self-repulsion, and the additional quartic LHY-induced self-repulsion. The review provides a comprehensive overview of the current understanding of QDs, their stability, and their potential applications in quantum systems.A new form of liquid matter: quantum droplets Quantum droplets (QDs) are robust two- and three-dimensional self-trapped states in Bose-Einstein condensates (BECs), stabilized by effective self-repulsion induced by quantum fluctuations around the mean-field (MF) states, known as the Lee-Huang-Yang (LHY) effect. This review summarizes recent theoretical and experimental results on QDs, focusing on their existence in binary and single-component BECs, and their stability with embedded vorticity. Theoretical models of QDs in three, two, and one dimensions are discussed, along with dimensional crossover from 3D to 2D and 1D. Experimental observations include stable 3D and quasi-2D QDs in binary BECs, and single-component QDs in dipolar condensates. Theoretical results highlight the stability of QDs with embedded vorticity, such as three-dimensional vortex rings and two-dimensional vortex rings and necklaces. Additionally, the review addresses the behavior of QDs in singular potentials and their stability against collapse due to the LHY effect. The review also discusses the creation of QDs in heteronuclear bosonic mixtures and their long lifetimes, which allow for the observation of intrinsic properties like self-evaporation. In single-component dipolar BECs, QDs are stabilized by long-range dipole-dipole interactions and contact interactions, including the LHY term. The review highlights the experimental realization of QDs in dysprosium and erbium atoms, demonstrating their stability and the emergence of interference fringes, indicating phase coherence. Theoretical and experimental findings confirm the possibility of creating stable QDs in binary BECs through the competition between cubic attraction and self-repulsion, and the additional quartic LHY-induced self-repulsion. The review provides a comprehensive overview of the current understanding of QDs, their stability, and their potential applications in quantum systems.