  In the past years several extensions of the canonical commutation relations
have been proposed by different people in different contexts and some
interesting physics and mathematics have been deduced. Here, we review some
recent results on the so-called {\em pseudo-bosons}. They arise from a special
deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is
replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. We start
discussing some of their mathematical properties and then we discuss several
examples.
