This dissertation describes reconstruction techniques in diffractive imaging when the data is exceptionally noisy and when crucial experimental parameters are unmeasured. In particular, this work focuses on two applications of diffractive imaging, single particle imaging with unoriented data and ultrafast magnetic imaging with unmeasured charge distribution, both of which are exciting experiments planned for free electron laser facilities. Concerning single particle imaging, in chapter 2 we introduce the EMC algorithm for reconstructing a particle's 3D diffraction intensity from very many photon-shot-noise limited 2D measurements, when the particle orientation in each measurement is unknown. We coin such an imaging technique cryptotomography. In this chapter, we also study the noise limits beyond which cryptotomography is impossible. This is followed by an experimental demonstration of EMC in chapter 3, where we reconstruct the 3D Fourier intensity distribution of mono-disperse prolate nano-particles using single-shot 2D diffraction patterns collected at DESYs FLASH facility when a bright, coherent, ultrafast X-ray pulse intercepted individual particles of random, unmeasured orientations. This experimental demonstration of cryptotomography extended the Expansion-Maximization-Compression (EMC) framework to accommodate unmeasured fluctuations in photon fluence and loss of data due to saturation or background scatter. In chapter 4 we discuss magnetic imaging. We study, using simulated experiments, the feasibility of phase retrieval in X-ray diffractive imaging of thin-film magnetic domains in the presence of intrinsic charge scattering given only photon-shot-noise limited diffraction data. We also chart out the limits of diffractive imaging when we vary both photon-shot-noise and the intensity of charge-scattering noise. This work is directly relevant to the time-resolved imaging of magnetic dynamics using coherent and ultrafast radiation from Xray free electron lasers.