Summary: We discuss a rather new phenomenon in chaotic dynamics connected with the fact that some three-dimensional diffeomorphisms can possess wild Lorenz-type strange attractors. These attractors persist for open domains in the parameter space. In particular, we report on the existence of such domains for a three-dimensional Hénon map (a simple quadratic map with a constant Jacobian which occurs in a natural way in unfoldings of several types of homoclinic bifurcations). Among other observations, we have evidence that there are different types of Lorenz-like attractor domains in the parameter space of the 3D Hénon map. In all cases, the maximal Lyapunov exponent \(\Gamma_1\) is positive. Concerning the next Lyapunov exponent \(\Gamma_2\) there are open domains where it is definitely positive, others where it is definitely negative and, finally, domains where it cannot be distinguished numerically from zero (i.e., \(|\Gamma_2| < \rho\), where \(\rho\) is some tolerance ranging between \(10^{-5}\) and \(10^{-6}\)). Furthermore, several other types of interesting attractors have been found in this family of 3D Hénon maps.