The nonlinear electrostatic and electromagnetic wave structures in pair-ion, multi-ion and dusty plasmas are studied. The reductive perturbation method (RPM) is employed with appropriate boundary conditions to derive the nonlinear partial differential equations to study the dynamics of nonlinear wave structures. The electrostatic nonlinear periodic (cnoidal) waves, solitons and shock wave structures are investigated in unmagnetized pair-ion (fullerene) plasma. The evolution equations for the first and second order nonlinear potentials are derived and steady state cnoidal wave solutions in terms of Jacobian elliptic functions and soliton solution of the Korteweg-de Vries (KdV) equation are presented. The nonlinear pair-ion flux associated with cnoidal waves is also derived. It is found that the small temperature difference between pair-ions appropriates the dispersion property of acoustic waves. Both compressive (hump) and rarefactive (dip) acoustic wave structures are obtained in pair-ion plasma. The conditions for monotonic shock structures for acoustic waves and shock with oscillatory trails at its wave front are also investigated. The dust-ion acoustic (DIA) cnoidal waves and associated nonlinear ion flux in the presence of negatively and positively charged dust particles are also studied. It is found that both compressive and rarefactive nonlinear structures exist when dust particles are negatively charged whereas only compressive structures are obtained for positively charged dust particles. It is also found that nonlinear ion flux is positive for compressive DIA cnoidal waves‟ case and is negative for rarefactive case. The two dimensional propagation of electrostatic ion-acoustic solitons for unmagnetized and magnetized multi-ion plasmas are studied. It is found that both fast and slow ion-acoustic waves can propagate in such a multi-ion plasma provided both ions are considered to be inertial and one of the ions component (light ions) is taken to be warm. The variations in the amplitude and width of the nonlinear slow and fast ion acoustic wave structures with density, temperature and magnetic field are investigated. Furthermore, magnetoacoustic cnoidal waves and solitons in magnetized plasma are also examined and plasma beta effects on nonlinear structures are discussed.