This is an announcement for the paper “The approximation property and Lipschitz mappings on Banach spacess” by Pilar Rueda<https://arxiv.org/find/math/1/au:+Rueda_P/0/1/0/all/0/1>, Enrique A. Sanchez-Perez<https://arxiv.org/find/math/1/au:+Sanchez_Perez_E/0/1/0/all/0/1>. Abstract: We present an overview to the approximation property, paying especial attention to the recent results relating the approximation property to ideals of linear operators and Lipschitz ideals. We complete the paper with some new results on approximation of Lipschitz mappings and their relation to linear operator ideals. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.02707