Fuel droplets represent strong inhomogeneities that are generally detrimental and intensify the stochastic behaviour of ignition. Still, the presence of small droplets has been found to decrease minimum ignition energies and enhance flame speeds. In this study, a comprehensive analysis of the phases of ignition in sprays is carried out in a controlled, well-characterised experiment: the initiation of a spherically expanding flame in a turbulent droplet-laden jet by a laser spark. A revision of definitions of ignition-related terms is proposed based on a critical time scale of the spark effects on the flame, evaluated from OH* visualisation, allowing for a distinction between the phases of kernel generation and flame growth. Based on the critical time scale, ignition failure time scales can be measured, as well as kernel sizes conditional on ignition or failure. Small kernels typically quenched faster than the critical time scale, characterising the short-mode failure. This mode was suppressed by increasing the laser energy and, consequently, the initial kernel size. Still, the ignitability of lean ethanol mixtures was only effectively improved through high-energy sparks and partial prevaporisation, with ignition being limited by breakdown. In jet fuel sprays, a suppression of short and long-mode failure occurred by decreasing the droplet size. In fact, by doing this, different flame propagation mechanisms were observed by OH/fuel PLIF. Both aviation fuels investigated – Jet A and a renewable alternative, ATJ-8 – exhibited similar flame speed behaviour due to changes in droplet size in each of the modes identified: the droplet, inter-droplet, and gaseous-like propagation modes. Concentrated reactions around large droplets found in lean conditions allowed for a slowly propagating flame front which ignited new droplets. Stoichiometric to rich conditions presented stronger evaporation at the flame and higher and more uniform heat release. Still, large droplets penetrated the flame, locally inducing regions of negative curvature and continuing to evaporate in the products. The droplet-induced effects disappeared at low SMD and rich conditions, giving rise to a fully gaseous layer at the flame and the highest flame speeds. Finally, insight and data from experiments are used to improve a low-order ignition model towards applications with sprays. Fuel fluctuations are modelled using a stochastic approach, and the extinction criterion of the model is calibrated. The model is then tested for an aviation gas-turbine combustor.