Liquid is the least understood state of matter from theoretical point of view among solids, liquids and gases. This is due to the strong interactions and large displacement in liquids compared to solids and gases and, consequently, the absence of a small parameter in liquids. The aim in this thesis is to gain some fundamental understanding of liquids and supercritical fluids on the basis of extensive molecular dynamics simulations. The work begins with revisiting the solid-like approach to liquid thermodynamics based on collective modes. The simulations provide the direct evidence that liquid energy and specific heat are well described by the temperature dependence of the Frenkel frequency. The agreement between predicted and calculated thermodynamic properties is seen in both subcritical and supercritical states. I subsequently detect the structural crossover of the medium-range order at the Frenkel line seen from the behaviour of the peaks of the pair distribution function. The results offer insights into inter-relationships between structure, dynamics and thermodynamics in liquids and supercritical fluids. I subsequently calculate the Grüneisen parameter (GP) in the supercritical state and find that it decreases with temperature from 3 to 1 on isochores depending on the density. The wide range GP results which includes the solid-like values - an interesting finding in view of the common perception of the supercritical state as being an intermediate state between gases and liquids. GP is also found nearly constant at the Frenkel line above the critical point. Collective modes above the Frenkel line at extreme supercritical conditions are studied. Direct evidence is presented for propagating longitudinal phononlike excitations with wavelengths extending to interatomic separations deep in the supercritical state. Finally, I address the thermodynamic crossover seen as the change of most important system properties such as energy and heat capacity at the Frenkel line.