We have developed several approaches to nuclear response functions based on the time-dependent density functional theory; real-time methods, finite-amplitude methods, QRPA for axially deformed nuclei, etc. We are aiming at systematic calculations from the proton- to neutron-drip lines. Thus, treatment of the continuum, self-consistent treatment of the deformation and pairing are important ingredients in our approaches. In this talk, we will show our recent developments and applications to nuclear photoabsorption cross sections and discuss properties of pygmy resonances in neutron-rich nuclei.