The study of manganese oxides, known as manganites, which exhibit the "Colossal" Magnetoresistance (CMR) effect, is a key area of research in the field of Strongly Correlated Electrons. Recent theoretical and computational studies have significantly advanced our understanding of these materials, revealing that their ground states are intrinsically inhomogeneous due to phase separation tendencies. This phase separation involves ferromagnetic metallic and antiferromagnetic charge and orbital ordered insulating domains. The resistivity versus temperature calculations using mixed states agree well with experimental results. The mixed-phase tendencies arise from electronic phase separation between phases with different densities and disorder-induced phase separation between equal-density phases. The coexisting clusters can be as large as micrometers. The phenomenology of mixed-phase states appears robust across different models, but the microscopic properties of the various manganite phases need further clarification. The review covers recent theoretical calculations addressing the complex spin, charge, and orbital ordered phases of manganites, as well as experimental results supporting these theoretical developments. The field of manganites, initially studied for ferromagnetism, has evolved to focus on the CMR effect, which is maximized at the boundary between the metal and insulator phases. The review discusses the phase diagrams and CMR effects in different manganite compounds, emphasizing the importance of phase separation and disorder in understanding the CMR effect. The theoretical and experimental work is converging towards a unified picture, highlighting the intrinsic inhomogeneities in manganites as key to their physics.The study of manganese oxides, known as manganites, which exhibit the "Colossal" Magnetoresistance (CMR) effect, is a key area of research in the field of Strongly Correlated Electrons. Recent theoretical and computational studies have significantly advanced our understanding of these materials, revealing that their ground states are intrinsically inhomogeneous due to phase separation tendencies. This phase separation involves ferromagnetic metallic and antiferromagnetic charge and orbital ordered insulating domains. The resistivity versus temperature calculations using mixed states agree well with experimental results. The mixed-phase tendencies arise from electronic phase separation between phases with different densities and disorder-induced phase separation between equal-density phases. The coexisting clusters can be as large as micrometers. The phenomenology of mixed-phase states appears robust across different models, but the microscopic properties of the various manganite phases need further clarification. The review covers recent theoretical calculations addressing the complex spin, charge, and orbital ordered phases of manganites, as well as experimental results supporting these theoretical developments. The field of manganites, initially studied for ferromagnetism, has evolved to focus on the CMR effect, which is maximized at the boundary between the metal and insulator phases. The review discusses the phase diagrams and CMR effects in different manganite compounds, emphasizing the importance of phase separation and disorder in understanding the CMR effect. The theoretical and experimental work is converging towards a unified picture, highlighting the intrinsic inhomogeneities in manganites as key to their physics.