  We derive transport-entropy inequalities for mixed binomial point processes,
and for Poisson point processes. We show that when the finite intensity measure
satisfies a Talagrand transport inequality, the law of the point process also
satisfies a Talagrand type transport inequality. We also show that a Poisson
point process (with arbitrary ${\sigma}$-finite intensity measure) always
satisfies a universal transport-entropy inequality \`a la Marton. We explore
the consequences of these inequalities in terms of concentration of measure and
modified logarithmic Sobolev inequalities. In particular, our results allow one
to extend a deviation inequality by Reitzner [31], originally proved for
Poisson random measures with finite mass.
