Whole-slide imaging systems can generate full-color image data of tissue slides efficiently, which are needed for digital pathology applications. This paper focuses on a scanner architecture that is based on a multi-line image sensor that is tilted with respect to the optical axis, such that every line of the sensor scans the tissue slide at a different focus level. This scanner platform is designed for imaging with continuous autofocus and inherent color registration at a throughput of the order of 400 MPx/s. Here, single-scan multi-focal whole-slide imaging, enabled by this platform, is explored. In particular, two computational imaging modalities based on multi-focal image data are studied. First, 3D imaging of thick absorption stained slides (∼60 µm) is demonstrated in combination with deconvolution to ameliorate the inherently weak contrast in thick-tissue imaging. Second, quantitative phase tomography is demonstrated on unstained tissue slides and on fluorescently stained slides, revealing morphological features complementary to features made visible with conventional absorption or fluorescence stains. For both computational approaches simplified algorithms are proposed, targeted for straightforward parallel processing implementation at ∼GPx/s throughputs.