Partial permutohedra are lattice polytopes which were recently introduced and studied by Heuer and Striker. For positive integers $m$ and $n$, the partial permutohedron~$\cP(m,n)$ is the convex hull of all vectors in $\{0,1,\ldots,n\}^m$ with distinct nonzero entries. In this talk I will present results on the face lattice, volume and Ehrhart polynomial of $\cP(m,n)$. This is joint work with Behrend, Castillo, Chavez, Diaz-Lopez, Harris and Insko.