The vibrational, thermodynamical and mechanical properties of solids are well-understood since Debye's work in 1912. On the contrary, the same understanding for amorphous systems (liquids and glasses) has remain elusive for more than a century and it is still a mystery. In this talk I will formulate a theory for liquids based on the so-called instantaneous normal modes and I will explain how their density of states and specific heat can be rationalized using simple effective concepts, in a way similar to Debye's theory for solids. Moreover, I will address the question about the differences between liquids and solids from the point of view of fundamental symmetries. I will propose a new distinction between solids and amorphous systems based on non-affine displacements and a topological symmetry which can be quantified by using the concept of Burgers vector applied to the dynamical displacement fields. I will show how effective field theory and hydrodynamics approaches based on this concept are able to derive from first principles all the known dynamical features of the vibrational modes in liquids. Finally, I will show an application of this formalism to understand and successfully quantify plasticity in amorphous systems.