abstract: We shall describe some recent results on Lorenz-like attractors as well on attractors with spiral geometry. In particular, we shall prove that the Hausdorff dimension of a geometric Lorenz attractor is strictly bigger than 2, a Log Law for the hitting time of expanding (as well contracting) Lorenz attractor. We apply these to obtain that the interior of the Lagrange spectrum of a geometric Lorenz attractor has non empty interior. These corresponds to joint work with V. Araujo, S. Galatolo, C. G. Moreira, I. Nisoli, S. Roma ̃na and M. Viana.