Water is the most abundant liquid on earth and also the substance with the largest number of anomalies in its properties. It is a prerequisite for life and as such a most important subject of current research in chemical physics and physical chemistry. In spite of its simplicity as a liquid it has an enormously rich phase diagram where different types of ices, amorphous phases and anomalies disclose a path that points to unique thermodynamics of its supercooled liquid state that still hides many unraveled secrets. In this review we describe the behavior of water in the regime from ambient conditions to the deeply supercooled region. The review is divided into sections that describe simulations and experiments on this anomalous liquid. Several scenarios have been proposed to explain the anomalous properties that become strongly enhanced in the supercooled region and they are described in the first section. Among those the second critical point scenario has been investigated extensively and at present most experimental evidence point to this scenario and it is described in the second section.Starting from the very low temperatures a coexistence line between a high density amorphous phase and a low density amorphous phase would continue in a coexistence line between a high density and a low density liquid phase terminating in a liquid-liquid critical point, LLCP. On approaching this LLCP from the one-phase region a crossover in thermodynamics and dynamics can be found. This is discussed based on a picture of a temperature-dependent balance between a high-density liquid and low-density liquid favored by, respectively, entropy and enthalpy leading to a consistent picture of the thermodynamics of bulk water. A section is devoted to ice nucleation since this is what severely impedes experimental investigation of the vicinity of the proposed LLCP. Experimental investigation of stretched water, i.e. water at negative pressure,gives access to a different regime of the complex water diagram. Different ways to inhibit crystallization through confinement and aqueous solutions are discussed through results from experiments and simulations using the most sophisticated and advanced techniques. These findings represent tiles of a global picture that still needs to be completed.The future direction section explores some of the possible experimental lines of research that are essential to complete this picture.