Although H₂ O has been the focus of a considerable amount of research since the beginning of the century, its peculiar physical properties are still not well understood. First we discuss some of the anomalies of this `complex fluid'. Then we describe a qualitative interpretation in terms of percolation concepts. Finally, we discuss recent experiments and simulations relating to the liquid-liquid phase transition hypothesis that, in addition to the known critical point in water, there exists a `second' critical point at low temperatures. In particular, we discuss very recent measurements at Tsukuba of the compression-induced melting and decompression-induced melting lines of high-pressure forms of ice. We show how knowledge of these lines enables one to obtain an approximation for the Gibbs potential G (P ,T ) and the equation of state V (P ,T ) for water, both of which are consistent with the possible continuity of liquid water and the amorphous forms of solid water.