\abstract 
A lecture presented at the 
von Neumann symposium on Quantization and
Nonlinear Wave Equations held at MIT in June, 1994.  
We describe the role of semigroups of 
endomorphisms of von Neumann algebras 
in algebraic formulations of quantum field theory, and
present a summary of recent developments in the theory
of $E_0$-semigroups. 
\endabstract