Lensless imaging is an imaging modality that allows high-resolution and large field-of-view (FOV) imaging with cost-effective and portable devices. In lensless imaging, the objects' complex amplitude information is computationally reconstructed from the diffracted intensity measured on a sensor plane. This holographic reconstruction has been traditionally implemented by iterative phase retrieval algorithms. However, due to the limited capability of the traditional algorithms, such as excessive processing time and high chance of failure in confluent specimens, lensless imaging has not been practically used in the relevant application areas. Here, we review the recent applications of deep learning (DL) algorithms in holographic image reconstruction that are proposed to achieve robust and fast holographic reconstruction in lensless imaging. These DL approaches include the supervised learning approach with paired training datasets and the unsupervised learning approach with unpaired training datasets or without any ground truth data. We also highlight some unique capabilities of the DL approaches, including lensless imaging with an extended depth-of-field (DOF) or virtual staining. Finally, we discuss new opportunities for exploiting domain adaptation techniques and physics-integrated approaches in lensless imaging.