Summary: Global attractivity and oscillatory behavior of the following nonlinear impulsive parabolic differential equation which is a general form of many population models \[ \begin{cases} {\partial u(t,x)\over\partial t}= \Delta u(t,x)-\delta u(t,x)+ f(u(t-\tau, x)),\;& t\neq t_k,\\ u(t^+_k, x)- u(t_k, x)= g_k(u(t_k, x)),\;& k\in I_\infty,\end{cases}\tag{\(*\)} \] are considered. Some new sufficient conditions for global attractivity and oscillation of the solutions of \((*)\) with Neumann boundary condition are established. These results are not only true but also improve and complement existing results for \((*)\) without diffusion or impulses. Moreover, when these results are applied to the Nicholson’s blowflies model and the model of Hematopoiesis, some new results are obtained.