Lensless digital holography is achieved by illuminating a specimen with partially coherent light and recording its diffraction pattern (or hologram). Since the diffraction pattern is measured at the sensor plane, reconstruction algorithms are needed to retrieve relevant data at the plane of interest. In principle, back-propagating the measured signal to the specimen plane by deconvolving with the point spread function (PSF) of the system would lead to perfect reconstruction if the measured signal was the full complex-valued diffraction pattern and the PSF of the system was known. However, the forward model is in principle not invertible due to the loss of phase information at the sensor plane, which makes reconstruction algorithms highly prone to artifacts. To alleviate this issue, we designed an artifact removal method based on techniques from sparse dictionary learning and coding [1], which was published in the 2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017). We then continued leveraging the sparse prior, as specimens such as blood or urine correspond to reconstructed images in which most of their pixels represent background as opposed to objects, by proposing an efficient reconstruction algorithm that directly attempts to retrieve the (unmeasured) phase of the hologram [3]. This work was published in the International Conference on Medical Imaging Computing and Computer-Assisted Intervention (MICCAI 2017). The proposed method generates high-quality reconstructions in a fully unsupervised way, however itrequires accurate knowledge about the imaging conditions and the optical parameters of the system. Recently, we have proposed a more robust version of this reconstruction method that is able to adapt the PSF of the system in a data-driven fashion [8]. This work was published in Optics Express.