In this talk I shall give an overview of the recent results on hyperbolic
systems of conservation laws with relaxation terms. 
Conservation laws describe physical phenomena where some
quantities are conserved. They can be used to model traffic flow, gas
dynamics, flow in porous media, etc... 
A brief introduction to conservation laws will be given, showing the
difficulties caused by the nonlinearity.

Relaxation problems arise when the conservation equations
also contain stiff source terms.  
They appear in several physical models,  
and also in  numerical schemes for computational purposes.

In the scalar case, under suitable assumptions
one can prove the existence of a weak entropy solution for the
relaxation equations.  The solutions have uniform BV bound, which
gives the convergence to a limit by a compactness argument. 
Error estimates can also be proved, both in one and in several
space dimensions. 
For systems with relaxation, however, uniform BV bounds are very difficult
to obtain.  At present, stability and convergence results are 
known only for the special class of "Temple systems". 
A probabilistic technique for deriving these BV bounds will be described.