The talk reviews some recent developments in the theory of quantum mechanical tunneling. The new phenomena discussed arise from the coupling of the tunneling system to a heat bath of temperature T. The question is how dissipation and thermal fluctuation affect the tunneling rate. Quantum tunneling proves to be very sensitive to these environmental influences. The results are not only important for the analysis of tunneling experiments in macroscopic systems but also provide a crucial test of various approaches put forward in the theory of quantum stochastic processes.