A strong and intermeshed electricity grid allows the cost-efficient achievement of renewable energy targets by enabling the use of favorable sites and by facilitating the balancing of stochastic infeed from renewables and electricity demand. However, construction of new lines is currently proceeding slowly in Europe. This paper quantifies the benefits of optimal transmission grid extensions for Europe up to 2050 by iterating an investment and dispatch optimization model with a load flow based grid model. We find that large grid extensions, allowing the full exploitation of the most favorable RES-E sites throughout Europe, are beneficial from a least-cost perspective. If the electricity network were to be cost-optimally extended, 228,000 km would be built before 2050 (+76% compared to today). Only for sites located furthest from large consumption areas in Central Europe would the value of grid extensions not always outweigh its costs. Furthermore, the capacity of transmission lines connecting favorable RES-E sites with demand centers is cost-optimally dimensioned to almost entirely export all RES-E generation that exceeds local electricity demand. Only in periods with the highest infeed of fluctuating renewables, electricity is stored. When optimal grid extensions are impeded, storage investments are chosen to a larger extent. (C) 2012 Elsevier Ltd. All rights reserved.