High-speed photography is a powerful tool for studying fast dynamics in photochemistry, spintronics, phononics, fluidics and plasma physics. Currently, the pump-probe method is the gold standard for time-resolved imaging, but it requires repetitive measurements for image construction and therefore falls short in probing non-repetitive or difficult-to-reproduce events. Here, we present a motion-picture camera that performs single-shot burst image acquisition without the need for repetitive measurements, yet with equally short frame intervals (4.4 trillion frames per second) and high pixel resolution (450 × 450 pixels). The principle of this method--'motion picture femtophotography'--is all-optical mapping of the target's time-varying spatial profile onto a burst stream of sequentially timed photographs with spatial and temporal dispersion. To show the camera's broad utility we use it to capture plasma dynamics and lattice vibrational waves, both of which were previously difficult to observe with conventional methods in a single shot and in real time.