There are two competing concepts in the literature for the integration of high shares of renewable energy: the coupling of electricity to other energy sectors, such as transport and heating, and the reinforcement of continent-wide transmission networks. In this paper both cross-sector and cross-border integration are considered in the model PyPSA-Eur-Sec-30, the first open, spatiallyresolved, temporally-resolved and sector-coupled energy model of Europe. Using a simplified network with one node per country, the cost-optimal system is calculated for a 95% reduction in carbon dioxide emissions compared to 1990, incorporating electricity, transport and heat demand. Flexibility from battery electric vehicles (BEV), power-to-gas units (P2G) and long-term thermal energy storage (LTES) make a significant contribution to the smoothing of variability from wind and solar and to the reduction of total system costs. The cost-minimising integration of BEV pairs well with the daily variations of solar power, while P2G and LTES balance the synoptic and seasonal variations of demand and renewables. In all scenarios, an expansion of cross-border transmission reduces system costs, but the more tightly the energy sectors are coupled, the weaker the benefit of transmission reinforcement becomes. (T. Brown) fuels such as hydrogen and methane (so called 'electrofuels'), or thermally [16]. Long-term storage can smooth out both the seasonal variations of renewables and the synoptic variations (∼ 3-10 days in the time dimension).Modelling all energy sectors in high spatial and temporal detail is computationally demanding. In order to maintain computational tractability, previous sector coupling studies have either focused on just a few demand sectors, or sacrificed spatial or temporal resolution.Studies of a few sectors have either considered just electricity and heat, electricity and transport, or electricity and gas. For example, in [17,18] the possibility of using excess renewable electricity in the heating sector was considered, but no requirements were set to defossilise all heating, or to couple to other demand sectors. In another set of studies, a simplified investment and dispatch scheme was used for a one-node-per-country model of Europe to study electricity-heat coupling [19]. Interactions between the electricity sector and transport were studied for electric vehicles in [20][21][22] and including fuel cell electric vehicles in [23,24]. More general coupling of electricity to gas for use in either heating or transport was considered in [25,26].Studies that include multiple sectors, often encompassing all energy usage, but that sacrifice spatial resolution have typically either considered single countries (e.g. Germany [27][28][29][30], , Ireland [34,35]) or considered the whole continent of Europe without any spatial differentiation [36] so that