We discuss unique features of lens-free computational imaging tools and report some of their emerging results for wide-field on-chip microscopy, such as the achievement of a numerical aperture (NA) of ∼0.8-0.9 across a field of view (FOV) of more than 20 mm(2) or an NA of ∼0.1 across a FOV of ∼18 cm(2), which corresponds to an image with more than 1.5 gigapixels. We also discuss the current challenges that these computational on-chip microscopes face, shedding light on their future directions and applications.