To investigate the cosmic future of the universe, first, we obtain the particle and event horizons, and their evolution in time for three well-known varying cosmological constant models. We investigate the implications of these varying cosmological constant models on the particle and event horizons, and their time evolution during the universe history and future. We study the behaviours around the origin and at the far future of the universe for all cases. Finally, we obtained the general behaviours of the horizons and time evolution functions with respect to the general scale factor a for each of the three cases of varying cosmological constant. The results show that for two of our three cases, a big bounce scenario is inevitable for the universe starting from the big bang and ending up with a bouncing re-collapse to its initial state.