Recently, strong coupling between light and matter has been realized in a variety of one-dimensional (1D) waveguide-QED experimental systems, which in turn makes them promising candidates for quantum information processing. Compared to cavity-QED systems, there is a new feature in waveguide-QED: the existence of a continuum of states, which brings in new physical effects, such as the bound-state effects. First, we study the fundamental interaction between local quantum objects, such as two-level systems and four-level systems, and photons confined in the waveguide. We show that the effective photon-photon interactions give rise to a variety of nonlinear optical phenomena such as photon blockade, creation of single-photon states and generation of spectrally entangled photons. Furthermore, based on our understanding of light-matter interactions in waveguide-QED, we investigate its implications in quantum information processing. In particular, we propose a new scheme for quantum computation using flying qubits—propagating photons in a one-dimensional waveguide—interacting with matter qubits.