To gain further insight into liquid water's structure and explore the role of different physical forces underlying the interaction between water molecules, the radial and angular structure of water is probed as a function of temperature for a carefully selected set of theoretical models. Simulations are performed with empirical rigid, empirical polarizable, empirical flexible with classical and quantum nuclei, and ab initio models with classical nuclei at 300 and 353 K and quantum nuclei at 300 K. The predicted radial distribution functions, spatial maps, and angular distributions of the neighboring water molecules are consistent with a model of liquid water in which water molecules are tetrahedrally coordinated. In addition, three-dimensional joint distribution functions are introduced and analyzed. By comparison of the functions obtained for hexagonal ice to those of liquid water, several thermally disordered, icelike cluster structures are identified in the fluid.