Marine phytoplankton constitutes about half of the primary production on Earth. It forms the base of the marine food web and is a pivotal player in the marine biological carbon pump. The primary environmental drivers that control phytoplankton growth are temperature, nutrient availability, light, and the concentration of inorganic carbon species. Ongoing climate change modifies these drivers, leading to a warming, high-CO2 ocean with altered nutrient availabilities and light regimes. Changes in phytoplankton productivity and community composition resulting from these newly emerging environmental states in the ocean have important implications for the marine ecosystem and carbon cycling. Biogeochemical ocean models are used to investigate how marine primary production may be affected by future climate change under different emission scenarios. Phytoplankton growth rates in models are typically determined by functions describing growth dependencies on temperature, light, and nutrients. However, a large body of laboratory studies on phytoplankton responses to environmental drivers reveals two points that are usually not considered in current biogeochemical models. Firstly, phytoplankton growth can be considerably modified by the state of the carbonate system. Changes in inorganic carbon species concentrations can be either growth-enhancing (CO2(aq) and bicarbonate are substrates for photosynthesis), or growth-dampening (increasing CO2(aq) levels lead to a shift in the carbonate equilibria and result in a pH decrease, a process which is called ocean acidification). Functions describing this growth dependence of phytoplankton on the carbonate system have not been implemented in large-scale ocean biogeochemical models so far. Secondly, growth responses towards one driver can be modified if the level of another driver is changing. Functions including these so-called interactive driver effects partly exist in models (e.g. the response to varying light levels may depend on the nutrient limitation term). However, the large number of laboratory studies on multiple driver effects has never been used to constrain driver interactions in large-scale ocean biogeochemical models. This holds especially true for the findings of growth responses to driver interactions that include ocean acidification, which make up the largest share of laboratory experiments. This thesis aims to investigate sensitivities of marine phytoplankton to changing CO2(aq) levels as well as to interactive effects between CO2 and other environmental drivers. A comprehensive and reproducible literature search in combination with a statistical analysis (Publication I) reveals that increasing CO2(aq) levels robustly dampen the growth-increasing effects of warming and improving light conditions. In addition, the results show that the calcifying phytoplankton group of coccolithophores experiences the strongest negative effects by ocean acidification compared to other phytoplankton groups. A second study (Publication II) examines the effects of mechanistically described carbonate system dependencies on primary production and community composition in a model. To this end, carbonate system dependencies of phytoplankton growth and and coccolithophore calcification are implemented into the global biogeochemical ocean model REcoM. The study shows that responses to ocean acidification cascade on growth responses to other drivers, which partly balance or counteract the direct impact of the carbonate system on growth rates. In addition, warming is identified as the main driver of the observed recent increase of coccolithophore biomass in the North Atlantic. A final study (Publication III) investigates the interactive effects between CO2 and temperature as well as between CO2 and light on phytoplankton biomass and community composition in a high emission scenario. For the parametrization in REcoM, growth responses to interacting drivers as synthesized in Publication I are used. The decrease of global future phytoplankton biomass and net community production by the end of the century is similar in simulations with and without driver interactions (-6% and -8%, respectively). However, phytoplankton responses to future climate conditions are considerably modified on a regional scale and the share of individual phytoplankton groups in the community changes both globally and regionally when accounting for multiple driver effects. Globally, diatoms and coccolithophores are impacted more and small phytoplankton less severely by future oceanic conditions when accounting for driver interactions. Future projections of the Southern Ocean phytoplankton community are modified most dramatically with the new interactive growth formulation, as diatoms and coccolithophores become less and small phytoplankton more abundant, while it is the other way round in simulations without driver interactions. The thesis highlights 1) that the carbonate system is a critical growth-modifying driver for phytoplankton in a high-CO2 ocean, which can furthermore modify growth responses to other drivers substantially, and 2) that driver interactions have considerable effects on climate-change induced alterations in the phytoplankton community as well as on regional biomass changes in a future ocean.