Neutron scattering is a powerful and versatile technique to probe spin-spin cor- relations in condensed matter physics. In this thesis, we present our work using neutron scattering to investigate the interplay of magnetism and superconductivity in the iron-based superconductor FeSe, the ground state of the quantum spin liquid candidate Ce2Zr2O7, topological magnons in BaNi2(AsO4)2, and the spin dynamics in the singlet-ground-state compound Ni2Mo3O8. In FeSe, superconductivity emerges from a nematic phase that breaks the in- plane four-fold (C4) rotational symmetry without magnetic ordering. Experimental and theoretical studies of this nematic phase attribute it to orbital ordering, spin fluctuations, or hidden magnetic quadrupolar order. We performed inelastic neutron scattering (INS) on an assembly of detwinned single crystals of FeSe to demonstrate that spin fluctuations are most intense at the antiferromagnetic wavevector QAF = (±1, 0) in the normal state, and the strong nematic anisotropy is also reflected in the spin resonance at QAF in the superconducting state. The electronic anisotropy of the nematic phase supports a highly anisotropic superconducting gap driven by spin fluctuation. Besides, in twinned FeSe, we use INS to study the effect of a magnetic field on spin resonance. Magnetic fields aligned along the c-axis broaden and suppress the spin resonance more efficiently than fields in the in-plane directions. Our results are consistent with the anisotropic effect of magnetic fields on the superfluid den- sity calculated in heat capacity measurements, which suggests that the resonance in FeSe is associated with the superconducting electrons arising from orbital-selective quasiparticle excitations between the hole and electron Fermi surfaces. Among spin systems where unpaired electrons form local spins, the quantum spin liquid (QSL) is an exotic one that does not magnetically order at all temperatures. The agreement of experiments and theories in one-dimensional (1D) systems proved the capability of neutron scattering to detect fractionalized quasiparticles. We carried out INS on single crystals of Ce2Zr2O7and revealed the presence of the hallmark of a QSL - a continuum of magnetic excitations - corresponding to fractionalized spinons at 35 mK. We combined heat capacity, muon spin relaxation, and AC susceptibil- ity measurements to demonstrate that Ce2Zr2O7is three-dimensional (3D) QSL with minimal magnetic and non-magnetic disorder. The bosonic analogs of topological fermionic quasiparticles arising from spin waves were reported in two-dimensional (2D) honeycomb lattice ferro/antiferromagnets and 3D antiferromagnets. We performed INS to study spin waves of the S = 1 honeycomb lattice antiferromagnet BaNi2(AsO4)2, which develops a zig-zag antiferromagnetic (AF) order below TN = 6 K, and determine the interactions with a Heisenberg model up to third-nearest neighbor exchange. The Dirac-like band crossing protected by the glide mirror symmetry was observed in the spectra. Singlet-ground-state systems, in which the crystal field ground state of the mag- netic ion is a singlet, are of great interest because the magnetic properties are sensitive to the ratio of magnetic exchange to single-ion anisotropy. We used thermodynamic and neutron scattering experiments to demonstrate that Ni2Mo3O8, a bipartite hon- eycomb lattice comprised of tetrahedral and octahedral Ni2+ environment, is a singlet- ground-state system. We found ferro- and antiferromagnetic excitonic flat bands in the neutron scattering spectra.