  Strongly interacting, dynamically disordered and with no small parameter,
liquids took a theoretical status between gases and solids. We review different
approaches to liquids and propose that liquids do not need classifying in terms
of their proximity to gases and solids. Instead, they are a unique system in
their own class with a notably mixed dynamical state in contrast to pure
dynamical states of solids and gases. We start with explaining how the
first-principles approach to liquids is an intractable, exponentially complex
problem of coupled non-linear oscillators with bifurcations. This is followed
by a reduction of the problem based on liquid relaxation time $\tau$
representing non-perturbative treatment of strong interactions. On the basis of
$\tau$, solid-like high-frequency modes are predicted and we review related
recent experiments. We demonstrate how these modes can be derived by
generalizing either hydrodynamic or elasticity equations. We comment on the
historical trend to approach liquids using hydrodynamics and compare it to an
alternative solid-like approach. We subsequently discuss how collective modes
evolve with temperature and how this affects liquid energy and other properties
such as fast sound. Here, our emphasis is on real, rather than model, liquids.
Highlighting the dominant role of high-frequency modes for liquid energy, we
review a wide range of liquids: subcritical low-viscous liquids, supercritical
state with two different dynamical and thermodynamic regimes separated by the
Frenkel line, highly-viscous liquids and liquid-glass transition. We also
discuss liquid-liquid phase transitions where the solid-like properties of
liquids have become further apparent. We then discuss gas-like and solid-like
approaches to quantum liquids and persisting theoretical problems. We list
areas where interesting insights may appear and continue the extraordinary
liquid story.
