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The low-energy physics of systems coupled to their surroundings is understoodby truncating to effective Hamiltonians; these tend to reduce to a fewcanonical forms, involving coupling to "baths" of oscillators or spins. Themethod for doing this is demonstrated using examples from magnetism,superconductivity, and measurement theory, as is the way one then solves forthe low-energy dynamics. Finally, detailed application is given to the excitingrecent Quantum relaxation and tunneling work in naomagnets.Comment: Chapter in "Tunneling in Complex Systems" (World Sci., edited T.  Tomsovic); 97 pages. Published in June 199

QUANTUM ENVIRONMENTS: SPINS BATHS, OSCILLATOR BATHS, and applications to QUANTUM MAGNETISM