Due to irreversible radiation damage, structure determination of biological macromolecules using X-rays is often done by taking snapshots from individual copies of the sample and assembling the snapshots in the end to solve the 3D structures. It is difficult to control the orientations of micron or sub-micron sized specimens when delivered to the X-ray beam. Furthermore, the signals in the snapshots may be so weak that each of them cannot be oriented separately. This thesis develops algorithms to address the task of 3D reconstruction from unoriented, noisy snapshots, with special focus on two X-ray methods. For the first one, single particle imagining at X-ray free electron lasers, we discuss the difficulty of orientation reconstruction of samples through computer simulation, and then present the analysis results of two experimental datasets. For the second technique, serial microcrystallography at synchrotron storage ring sources, we first describe the development of our reconstruction algorithm through two proof-of-concept studies. In these studies, diffraction patterns were collected from large protein crystals to simulate the signal level of those collected from protein microcrystals at storage ring sources. Finally, we demonstrate our method by solving a protein structure from microcrystal diffraction patterns collected at a storage ring synchrotron source. These data would have been discarded by crystallographers because of their weak signals. Through the detailed presentation of the analysis processes, this thesis is also meant to be a self-contained tutorial on reconstruction problems using X-ray sources.