In the last decades, X-ray phase-contrast imaging has proven to be a powerful method for unveiling the inner structure of samples and is capable of visualising even minute density differences. Recently, speckle-based imaging (SBI), the youngest X-ray phase-sensitive technique, has received great interest due to its high sensitivity, quantitative character and relaxed requirements on the setup components and beam properties. This thesis is focussed on the development, experimental optimisation and applications of SBI, with the aim of simplifying its implementation, increasing its flexibility and expanding its potential.For this, a robust, flexible data acquisition and reconstruction approach, the unified modulated pattern analysis (UMPA), was developed, which lifts previous constraints of SBI. UMPA allows for tuning of the sensitivity and spatial resolution by adjusting the scan and reconstruction parameters. It is applicable not only to random speckle, but also periodic interference patterns, bridging the gap and improving the performance of both speckle-and single-grating-based techniques.Following the first demonstration of UMPA, its potential for a range of applications is illustrated in this thesis. It is shown that UMPA can be employed for X-ray optics characterisation to quantify aberrations in the focussing behaviour of X-ray refractive lenses with high precision and accuracy. UMPA phase tomography is applied to the field of biomedical imaging for high-sensitivity three-dimensional (3D) virtual histology of unstained, hydrated soft tissue, giving unprecedented structural and quantitative density information.Further developments of SBI explored in this thesis include the testing of novel customisable speckle diffusers, the extension of SBI to higher X-ray energies for geology and materials science applications, and the demonstration of UMPA at a laboratory X-ray source. These progresses promise new possibilities of SBI for high-sensitivity, robust and high-throughput imaging in previously inaccessible fields and make SBI accessible to a wider range of users in research and industry.