Ultrafast ultrasound imaging enables high frame rates by transmitting unfocused wavefronts such as plane waves (PWs). While enabling visualization of fast physiological processes, it suffers from degraded image quality compared to conventional focused acquisitions. These limitations are amplified in portable and wireless ultrasound systems, which are increasingly adopted for point-of-care imaging. Their compact design imposes strict constraints on hardware complexity, data bandwidth, and power consumption, further challenging image quality. In this context, deep learning has emerged as a powerful strategy to enhance image reconstruction. This thesis investigates the use of convolutional neural networks (CNNs) to improve ultrafast ultrasound image quality in both full-array and undersampled acquisition settings relevant to portable ultrasound systems. The first part focuses on supervised learning strategies to enhance the quality of single PW images, aiming to match the image quality achieved by coherent PW compounding. This part begins by examining the choice of training data, using simulated or in vivo images. Results demonstrate that models trained on simulated data perform poorly on in vivo data, revealing a domain gap. To improve in vivo performance, we propose a loss with a Kullback-Leibler divergence component that handles the high dynamic range of radio frequency (RF) ultrasound data and preserves echogenicity. Using this loss, transfer learning proves highly effective in mitigating domain gaps between simulated and in vivo datasets and across distinct acquisition configurations. Experiments confirm that CNN-based enhancement generalizes to moderate variations in transducer characteristics and unseen anatomical regions, highlighting the model's robustness. The framework is further adapted to process complex-valued in-phase and quadrature data. The second part of the thesis extends the deep learning framework to sparse-array acquisitions, which reduce data volume-a key requirement for ultra-portable systems. A sequential CNN strategy is proposed to progressively enhance images acquired with a limited number of transducer elements, yielding improvements in image quality compared with single CNN models. Building on these results, an inpainting framework is introduced to reconstruct missing RF signals prior to beamforming. Experimental results show that learning directly from pre-beamformed RF data yields better reconstruction quality than image-domain approaches, improving structural accuracy and phase coherence. The dual-domain loss function, which integrates signal- and image-domain information through a model-based reconstruction term, further enhances quality. The robustness of the method is assessed across different sampling strategies and transducers. Finally, the approach is extended to multi-PW acquisitions and quantitative imaging, where it generalizes effectively to steered PWs and enables accurate speed-of-sound estimation under sparse sampling conditions. Overall, this work demonstrates that both careful training dataset selection and operating in the signal domain-rather than the image domain-are critical for the successful application of deep learning in ultrafast ultrasound imaging. The proposed frameworks establish deep learning-based RF inpainting as a powerful tool for achieving efficient, high-quality, and physically consistent imaging, paving the way for the next generation of ultra-portable ultrasound systems.