We often refer to the magnetic dipoles as spins. The simplest model describing interactions between spins, is the Ising Model,proposed by E. Ising in 1925. Dynamics of Ising models is a much studied phenomenon and has emerged as a rich field of present-day research. An important dynamical feature commonly studied is the quenching phenomenon below the critical temperature. We have studied the zero temperature quenching dynamics of different Ising spin systems. First we have studied the zero temperature quenching dynamics of two dimensional Ising spin system with competing interactions. Then we have studied the effect of the nature of randomness on zero temperature quenching dynamics of one dimensional Ising model. Many dynamical models related to social phenomena like opinion formation in a society can be described in terms of spin models. A model for opinion dynamics has been proposed in which the binary opinions of the individuals are determined according to the size of their neighbouring domains. This model can be equivalently defined in terms of Ising spin variables and the various quantities studied have one to one correspondence with magnetic systems.