Clouds have a strong net cooling effect on our planet, as they reflect a large part of the incident solar radiation. To be able to make accurate forecasts of the global climate, cloudiness should therefore be correctly represented by climate models. Currently, however there are large differences in the forecasted temperature increase among climate models. One of the most important causes of these differences is the uncertainty in the representation of clouds, in particular of stratocumulus clouds. Stratocumulus clouds are low clouds that often form an almost completely closed cloud deck. Only little sunlight passes through them, so that they are often associated with grey and dull weather. Stratocumulus clouds are frequently found over oceans in the subtropics, where they can cover enormous areas of several millions of square kilometers. When they are advected by the trade winds from the subtropics toward the equator, a transition typically occurs during which the stratocumulus slowly thins and eventually breaks up. Simultaneously, cumulus clouds appear that have a much lower cloud cover and therefore reflect less sunlight. Hence, stratocumulus transitions cause an abrupt decrease of the cloud-induced net cooling effect, which makes them particularly important for climate models. At the same time, the representation of stratocumulus clouds is extremely challenging for climate models, since their development strongly depends on the transport of among others moisture by small-scale turbulence. Due to their coarse resolution, climate models are unable to explicitly simulate processes with typical sizes of a hundred kilometers or less. Hence, turbulent transport, together with other cloud related processes, is represented in a simplified statistical manner by parameterizations, which introduces much uncertainty. During this thesis project we have simulated stratocumulus clouds and their transitions with a numerical model that, in contrast to climate models, is capable of representing the interaction between turbulence and clouds in detail. In chapter two we compare the results of six of these so-called large-eddy simulation models with measurements that had been gathered during a stratocumulus transition. All models are shown to be capable of correctly representing the main features of the transition, including the slow thinning of the stratocumulus and the simultaneous development of cumulus clouds. The simulations yield a wealth of data on the three-dimensional structure of the atmosphere, which is impossible to obtain from measurements. These data allow us to investigate the causes of the thinning and breaking up of stratocumulus clouds during transitions in detail. One of these causes can be sought in the change of the turbulent structure of the atmospheric boundary layer in which the stratocumulus resides. At the start of the transition, the boundary layer is still rather shallow, allowing turbulence to vertically mix the air in it relatively well. Hence, the moisture that evaporates from the ocean surface can easily reach the cloud layer, thereby feeding and maintaining it. As the transition progresses, the boundary layer becomes deeper and the distance between the clouds and the surface increases. It has been suggested that eventually turbulence will not be sufficiently strong anymore to maintain the well-mixed structure of the boundary layer. This so-called decoupling would cause the moisture transport to the stratocumulus to be almost completely cut off, causing it to rapidly dry and dissolve. However, in chapter two we show from the model results that decoupling has less effect on the humidity transport than was originally thought. Another process that is often held responsible for the breaking up of stratocumulus clouds is entrainment. In this process, air from the relatively warm and dry free troposphere is mixed into the boundary layer. Hence, entrainment causes drying and warming of the stratocumulus cloud and is therefore associated with its thinning. In chapter three we derive an equation that describes the change with time of the total amount of condensed water in the cloud. Using this equation we argue that entrainment is indeed an important cause for the thinning of stratocumulus clouds during a transition. On the other hand, we also show that other processes, such as the supply of moisture from the sea surface, can be strong enough to diminish this thinning, even for conditions for which earlier studies predicted an unconditional breakup of the cloud. In the second part of this thesis, we investigate the effect of the warming of the climate on stratocumulus clouds. In chapter four, we perform a set of simulations of stratocumulus clouds for conditions that are representative for the current climate. In a second set of simulations we mimic a future climate by increasing the temperature of the atmosphere and of the sea. This idealized climate perturbation causes a decrease of the thickness and hence the reflectivity of the stratocumulus clouds in all simulations. This suggests that, in a future climate, more solar radiation will be able to reach the Earth's surface than in the current climate. This way, stratocumulus clouds will enhance the warming of the climate. As a result of a warming of the climate, the large-scale atmospheric circulation between the equator and the subtropics, the so-called Hadley circulation, will weaken. In chapter five we show that a weakening of the Hadley circulation delays the breakup of stratocumulus clouds during transitions. Effectively, this leads to an increase of the amount of stratocumulus clouds in a future climate. This mechanism therefore counteracts the reduction of the amount of stratocumulus clouds in response to a climate warming that we found in chapter four, but will likely not be strong enough to completely compensate for it.