The European Union in 2011 has developed a roadmap for moving to a competitive low carbon economy in 2050, which provides a long term pathway to achieve an 80% cut in domestic emissions compared to 1990 by 2050 (European Commission, 2011). Considering the Paris COP 21 agreement, the reduction in CO2-emissions will need to be definitely higher than the previously envisaged 80%. The building sector provides a high potential to contribute to this target. The main research question of this doctoral thesis is: What are the perspectives to increase the energy performance in the building sector? Four case studies are presented addressing different methodology approaches, building sectors, countries, policies and economic framework. Firstly, cost curves for selected European countries building stock are derived to show cost and benefits of energy efficiency solutions and related energy saving for space heating by 2030. ^Secondly, policy based energy demand scenarios to 2050 are modelled and their consistency with Paris COP21 decarbonisation targets is tested. Thirdly, buildings and energy efficiency solutions for the Lithuanian residential building sector are identified which have to be addressed by policy makers in order to achieve high energy savings in the most-cost effective way. And fourthly, the current and future energy demand in the European shopping centre building stock is investigated. The calculation of the final energy demand (for space heating and hot water) is based on a bottom-up approach taking into account disaggregated building stock data. Two different models are applied, the existing Invert-EE/Lab model and a newly developed Cost Curve Tool. Invert/EE-Lab is a dynamic bottom-up techno-socio-economic simulation tool that evaluates the effects of different policies on the future energy demand in the building sector. ^The Cost Curve Tool provides different types of cost curves aiming to show the cost and energy related benefits of investments in energy efficiency solutions. Energy efficiency improvements of the building sector provide a high potential to reduce its energy demand by 2030 and 2050. However, the economic energy saving potential in the building sector varies from one country to another. This is due to the following key parameters for the energy savings; current energy performance of buildings, renovation rates and depth, policy packages and energy prices. The main drivers of the CO2-emission reduction in the building sector are the renovation rate and depth, the heating system exchange rate and the substitution of the fossil energy based heating systems with renewable systems. The target of keeping the increase in global average temperature below 2C set in Paris Agreement requires the CO2-reductions beyond 80-90% in the building sector. ^The results show that an achievement of COP21 agreements require higher policy ambitions, going beyond the assumptions of ambitious policy scenarios developed in this thesis.