Abstract: Quantum transport in a lattice is distinct from its counterpart in continuum media. Even a free wave packet travels differently in a lattice than in the continuum. We describe quantum scattering in a one-dimensional lattice and illustrate characteristics of quantum transport such as resonant transmission. In particular we examine the transport characteristics of a random trimer model. We demonstrate the real-time propagation of a wave packet and its phase shift due to impurity configurations. Spin-flip scattering is also taken into account in a spin-chain system. We show how individual spins in the chain evolve as a result of a spin-flip interaction between an incoming electron and a spin chain.