Magnetite (Fe$_3$O$_4$) is the first magnetic material discovered by mankind. Despite thousands of years of applications, from the magnetic compass to data storage, and decades of basic research, it remains among the most fascinating materials for physicists. The most important reason for the continuous interest in magnetite is the occurrence of discontinuous changes in its ground state around 120 K, the so-called Verwey transition, characterized by profound modifications in the electronic structure, mutually related to atomic displacements. The remarkable complexity of the transformation process still leaves open fundamental problems in the understanding of the microscopic mechanism of the Verwey transition. Further research efforts are needed to better describe the nature of the elementary excitations at the origin of the initial instability, how it propagates in different degrees of freedom and its relationship to precursor phenomena. This Thesis combines together the potentials of steady-state and time-resolved spectroscopy to study the critical dynamics of the lattice vibrations, and the fluctuations of electronic and structural order across the Verwey transition. Their signatures are identified in the coherent response of the optical functions to ultrashort laser pulses, and the inelastic scattering of light and neutrons, which provide complementary information, with selective sensitivity to different types of elementary excitations. Among the most important results, we manage to observe in the energy and time domain critical modes with different interplay of charge distribution and atomic displacements, and diffusive dynamics, typical of an order-disorder process.