In joint work with E. R. Speer and J. L. Lebowitz, we consider two-species variants of the totally asymmetric simple exclusion 
 process (TASEP) on a finite one-dimensional lattice. Introducing one more class of particle is not as arbitrary as it may seem 
 at first bite:Second-class particles were discovered to be very useful in understanding the behaviour of shock profiles in the 
 single species TASEP. Most of the time will be spent discussing an "integrable" variant in which second-class particles are not
 allowed to leave. Time permitting, we will consider other variants which permit exact analysis.