The radiation dosage delivered to the sample is a constant challenge facing X-ray imaging systems. In conventional transmission-based computed tomography (CT), a beam penetrating through thick, high-attenuation region in the sample results in low signal on the detector, and therefore a higher power (e.g., tube current modulation) or longer integration time is often required to maintain signal quality. The issue of radiation dose becomes more sever in coherent scattering X-ray tomography, in which the scattering signal is typically orders of magnitude weaker than the transmitted beam. With X-ray photon-counting detectors, transmitted (or scattered) X-ray photons can be acquired at extremely low photon flux, which enables us to greatly reduce the imaging time and dose administrated to the sample. Instead of counting the average the number of photons within a fixed time interval, the arrival times of only a few photons detected in sequence contain sufficient information to estimate the attenuation (or scattering) property, which allows object reconstruction based on our measurement geometry and noise model. We will also discuss compressive or adaptive data acquisition schemes to implement material identification utilizing the energy sensitivity of X-ray photon-counting detector. Our method can be further parallelized with a photon-counting detector array to achieve fast, low-dose X-ray tomographic imaging based on either attenuation or scattering signals, which could find broad applications in medical diagnosis and security screening.