Magnetic Resonance Imaging (MRI) is a non-invasive, non-ionizing imaging modality with unmatched soft tissue contrast. However, compared to imaging methods like X-ray radiography, MRI suffers from long scanning times, due to its inherently sequential acquisition procedure. Shortening scanning times is crucial in clinical setting, as it increases patient comfort, decreases examination costs and improves throughput. Recent developments thanks to compressed sensing (CS) and lately deep learning allow to reconstruct high quality images from undersampled images, and have the potential to greatly accelerate MRI. Many algorithms have been proposed in the context of reconstruction, but comparatively little work has been done to find acquisition trajectories that optimize the quality of the reconstructed image downstream. Although in recent years, this problem has gained attention, it is still unclear what is the best approach to design acquisition trajectories in Cartesian MRI. In this thesis, we aim at contributing to this problem along two complementary directions. First, we provide novel methodological contributions to this problem. We first propose two algorithms that improve drastically the greedy learning-based compressed sensing (LBCS) approach of Gözcü et al. (2018). These two algorithms, called lazy LBCS and stochastic LBCS scale to large, clinically relevant problems such as multi-coil 3D MR and dynamic MRI that were inaccessible to LBCS. We also show that generative adversarial networks (GANs), used to model the posterior distribution in inverse problems, provide a natural criterion for adaptive sampling by leveraging their variance in the measurement domain to guide the acquisition procedure. Secondly, we aim at deepening the understanding of the kind of structures or assumptions that enable mask design algorithms to perform well in practice. In particular, our experiments show that state-of-the-art approaches based on deep reinforcement learning (RL), which have the ability to adapt trajectories on the fly to patient and perform long-horizon planning, bring at best a marginal improvement over stochastic LBCS, which is neither adaptive nor does long-term planning. Overall, our results suggest that methods like stochastic LBCS offer promising alternatives to deep RL. They shine in particular by their scalability and computational efficiency and could be key in the deployment of optimized acquisition trajectories in Cartesian MRI