Flow cytometry, incorporating either point- or imaging-based detection schemes, is recognized to be the gold-standard tool for high-throughput manipulation and analysis of single cells in flow but is typically limited in either the number of cells that can be interrogated per unit of time or the resolution with which individual cells can be imaged. To address these limitations, we present a sheathless, microfluidic imaging flow cytometer incorporating stroboscopic illumination for blur-free cellular analysis at throughputs exceeding 50,000 cells/s. By combining inertial focusing of cells in parallel microchannels and stroboscopic illumination, the chip-based cytometer is able to extract multi-color fluorescence, bright-field, and dark-field images and perform accurate sizing of individual cells and analysis of heterogeneous cell suspensions while maintaining operational simplicity. To showcase the efficacy of the approach, we apply the method to the rapid enumeration of apoptotic cells and the high-throughput discrimination of cell-cycle phases.