In this talk I will discuss some recent works on the bubbling phenomena for approximate biharmonic maps in dimension 4. For general target manifolds, we obtain an energy identiy for weakly convergent sequences of approximate biharmonic maps whose bitension fields are bounded in $L^p$ for $p>4/3$, which can be improved to $p>1$ when the target manifold is a round sphere. As an application, the energy identity is obtained the heat flow of biharmonic maps in 4 dimension at the time $t=/infty$.