GeV pulsar and TeV pulsar wind nebulae represent the largest Galactic population in the GeV and TeV regime respectively. Even when sharing the same central engine, that is, an energetic and young pulsar, the processes ruling the two regimes largely differ. At GeV energies, the radiation is pulsed and the environment conditions on the pulsar magnetosphere and pulsar wind prevail. At TeV energies, the steady, integrated over time, nebula outshines. Nevertheless those processes should be ultimately connected being different aspects from a continuous pulsar/PWNe system. We will review the state-of-the-art knowledge on these objects and describe in a quantitative manner the general trends observed experimentally. We will also discuss the experimental techniques used now-a-days to detect gamma-rays at very-high energies with particular emphasis in the Cherenkov Telescope Array (CTA) observatory.