The aim of this paper is to showcase different decarbonization pathways for Germany and Europe withvarying Carbon dioxide (CO2) constraints until 2050. The Global Energy System Model (GENeSYS-MOD)framework, a linear mathematical optimization model, is used to compute low-carbon scenarios forEurope as a whole, as well as for 17 European countries or regions. The sectors power, low- and high-temperature heating, and passenger and freight transportation are included, with the model endogenouslyconstructing capacities in each period. Emission constraints differ between different scenarios and areeither optimized endogenously by the model, or distributed on a per-capita basis, GDP-dependent, orbased on current emissions. The results show a rapid phase-in of renewable energies, if a carbon budgetin line with established climate targets is chosen. In the 2°pathway, the power and low-temperatureheat sectors are mostly decarbonized by 2035, with the other sectors following. Wind power is the mostimportant energy source in Europe by 2050, followed by solar energy and hydro power. The heatingsector is dominated by biogas and heat pumps, while electric vehicles emerge in the transportation sectorin the later periods. Differences in renewable potentials lead to different developments in the regions,e.g., converting Germany from a net exporter of electricity into an importing country by 2050. In the1.5°pathway, not all calculations are feasible, showcasing that especially countries like Poland or theBalkan region that heavily rely on fossil fuels will face difficulties transitioning away from their currentgeneration capacities. It can, however, be shown that the achievement of the 2°target can be met with lowadditonal costs compared to the business as usual case, while reducing total emissions by more than 30%.