Microscopic dynamical events control many of the physical processes at play in condensed matter: transport, magnetism, catalysis and even function of biological assemblies. Inelastic (INS) and Quasi-Elastic Neutron Scattering (QENS) are irreplaceable probes of these phenomena. These experimental techniques reveal the displacements of atoms and molecules over distances spanning from angstroms to a few tens of nanometers, on time scales ranging from a fraction of picoseconds to microseconds. In this context, the different INS and QENS machines (Time-of-Flight (ToF), Backscattering (BS) and Neutron spin-echo (NSE)) stand at a central position. After introducing an underlying basic theoretical toolbox for neutron scattering, the principles and key elements of a ToF measurement are described. While, here, we mainly focus on disk choppers spectrometers, all the INS/QENS instruments share a common ground: they directly and simultaneously probe correlation functions in both time and space, so that the scattering vector (Q) dependence of the systems characteristic time(s) can be measured. To illustrate, the potentialities of the technique in the field of soft-matter, we show a multiscale approach of the dynamics of a polymer melt. The system is probed from the molecular to the mesoscopic scale (1 ps to 0.6 μs and 0.1 to 40 nm), in bulk and under nanometric confinement. We address the different dynamical modes of a high mass entangled polymer chain: local monomer dynamics, Rouse modes up to the reptation process. This study exemplifies that, used in conjunction with hydrogen/deuterium isotopic effects, high resolution QENS can be bridged to the Zero Average Contrast (ZAC) method to probe, in a non destructive way, the dynamics of a single polymer chain in bulk but also under severe nanometric confinement. Connection and complementarity of the neutron derived analysis with Pulsed-Field Gradient and Relaxation NMR techniques are discussed.