Active matter, which is a physical abstraction of running animals, flying birds, marching locusts, swimming bacteria, migrating cell and even cytoskeleton, has been a new building block for physicists over the last decade or so to understand the common collective behavior in these non-equilibrium systems. The liquid crystal state of active matter is of particular interesting since the collective dynamics is coupled with large scale liquid crystal order. Dynamic instabilities are widely observed in active liquid crystal systems. This often leads to large-scale collective motion in active nematics. Here we would like to show the interesting dynamical properties of two model active nematic systems when instabilities take place.[1-2] In a toy active nematic system where the interaction only tends to align intersecting needle particles, we predict long-wave length instabilities and further show large-scale chaotic evolution in such system. We also use hard elliptic rods instead of penetrable toy needles to simulate active nematic state. We find the instability in deep nematic order is characterized by the active unbinding of topological defects. These defects behave very differently to non-active systems. We further reveal that their anomalous dynamics may lead to large-scale collective motions in such active liquid crystal system.