Dark-Field X-ray Imaging allows X-ray imaging systems to detect information about features in a sample which would otherwise be undetectably small. Scattering from these microstructures is detected rather than resolving them directly – if the features causing the scattering have some orientation, the scattering can be orientated. Directional dark-field imaging can be used to measure this, allowing information on the orientation to be measured. Speckle-Based Imaging is a technique capable of detecting these signals by using an object to create a random intensity pattern in the X-ray beam. Tracking how the sample modifies this pattern allows for phase-contrast and dark-field images to be extracted. In this thesis, we present a new algorithm for extracting the directional dark-field signal from speckle-based imaging data: the Directional Dark-Field modification to the Unified Modulated Pattern Analysis (DDF-UMPA) Algorithm. At our proof-of-principle synchrotron-based experiment, we show it can be used to measure the orientation of carbon fibres to within one degree of accuracy. We then optimise a customised liquid-metal-jet X-ray source based laboratory setup for speckle-based imaging. We demonstrate that the DDF-UMPA algorithm is compatible with this setup, before attempting to demonstrate the technique is compatible with a conventional, commercial, microfocus X-ray CT system. We show progress towards developing our own customised optical elements to pattern the beam. We then demonstrate compatibility with the periodic intensity patterns used in beam-tracking dark-field X-ray imaging systems. Many of the experiments described in this thesis use composite materials as samples in order to demonstrate the potential applications for directional (and scalar) dark-field imaging within this field. We demonstrate these techniques can be used to detect fibre orientations and detect low-velocity impact damage.