  Let $(M,J)$ be a $2n$-dimensional almost complex manifold and let $x\in M$.
We define the notion of almost complex blow-up of $(M,J)$ at $x$. We prove the
existence of almost complex blow-ups at $x$ under suitable assumptions on the
almost complex structure $J$ and we provide explicit examples of such a
construction. We note that almost complex blow-ups are unique. When $(M,J)$ is
a $4$-dimensional almost complex manifold, we give an obstruction on $J$ to the
existence of almost complex blow-ups at a point and prove that the almost
complex blow-up at a point of a compact almost K\"ahler manifold is almost
K\"ahler.
