Let \((N_1,h_1)\), \((N_2,h_2)\) be Riemannian manifolds of positive dimensions \(n_1\), \(n_2\). If \(f\) is a positive valued function on \(N_1\), then the product manifold \(N_1\times N_2\) equipped with the warped product metric \(h_1+ f^2 h_2\) is called a warped product manifold \(N_1\times_f N_2\) with warping function \(f\). The author treats the following realization problem: Which manifolds of the above type can be immersed as affine hypersurfaces in some affine space, so that the induced fundamental form \(h\) coincides with the Riemannian metric \(h_1+ f^2 h_2\)? Two existence theorems proved by the author show that there exist many manifolds of the above type, which can be realized either as graph hypersurfaces (constant transversal vectorfield) or centroaffine hypersurfaces (centroaffine normalization). Especially, every warped product surface can be realized as a graph surface or as a centroaffine surface in \(\mathbb{R}^3\). Secondly, inequalities in terms of the warping function and the Chebyshev vector field are established which have to be fulfilled if a warped product manifold \(N_1\times_f N_2\) can be realized as a centroaffine hypersurface or as a graph hypersurface. The equality case leads to proper and improper affine hyperspheres, respectively.