The gasoline compression-ignition (GCI) concept has been proposed in recent years to circumvent the typical diesel engine NOx and soot emissions trade-off, whilst maintaining high engine efficiency. The GCI concept is commonly realised in a conventional diesel engine with heated intake air, utilising a conventional injection system and a single low-reactivity gasoline-like fuel. Combustion phasing is controlled through the injection timing, while the fast and lean combustion enables very high brake efficiency in excess of 50% with low NOx/particulate emissions across a wide range of engine loads. Additionally, this combustion mode can utilise economical and potentially widely available low-grade gasoline fuels (naphtha) with octane numbers in the range of 70-80. Despite many advantages, the ignition timing and combustion rate of GCI are very sensitive to both fuel chemistry and engine operating conditions. The lack of a fundamental understanding of ignition and combustion behaviours limits the optimisation of GCI engines. The aim of this thesis was to advance the fundamental understanding of the GCI combustion process. Characteristics of fuel-oxidiser mixing, ignition and combustion processes for gasoline-like fuels with a range of octane rating at compression-ignition (CI) engine relevant conditions were investigated. Experiments were conducted in an optically accessible constant-volume combustion chamber (CVCC), featuring well-characterised quiescent charge throughout the injection and combustion events. A single-hole axial-drilled diesel injector mounted on the back wall of the CVCC was used for fuel injections. The first part aims to assess the combustion characteristics of iso-octane (a gasoline surrogate) at CI conditions. CVCC featured an ambient gas density of 22.8 kg/m3 and an O2 concentration of 21 vol.\%. Optical techniques including natural flame luminosity, OH* chemiluminescence and shadowgraph imaging were performed to compare the combustion characteristics over ambient gas temperatures from 1000 K to 1120 K Measurements were also performed for n-heptane (a diesel surrogate) for reference purposes. Formaldehyde (CH2O) planar laser-induced fluorescence (PLIF) imaging was performed to confirm the presence of low-temperature reactions across the jet head, prior to the high-temperature ignition of iso-octane. From the measurement results, the lift-off lengths (LOLs), ignition delays (IDs) and their corresponding uncertainties for both fuels are observed to increase with lowering ambient temperature conditions. The LOLs, IDs and their uncertainties for the iso-octane flames are also consistently measured to be higher than that of n-heptane, across the tested ambient temperature range. The results reveal that the highest variability detected for the flame stabilisation distance of the iso-octane flame at the lowest tested ambient temperature condition 1000 K is attributable to the long transient stabilisation phase that it exhibits after ignition. Additional tests performed using a single-injection test case with lower octane number fuel, as well as split-injection strategies with neat iso-octane as fuel, demonstrate their potential to reduce the transient stabilisation phase of the test flames when compared with single-injection test case with neat iso-octane as fuel. The second part aims to investigate the effect of laser-induced plasma ignition (LI) on combustion behaviours of iso-octane at compression-ignition conditions. A high-energy laser was used to force the fuel ignition at a quiescent-steady environment inside the CVCC with 900 K ambient gas temperature, 22.8 kg/m3 ambient gas density and 21 vol.% O2 concentration. The diesel surrogate (n-heptane) was tested at a lower charge temperature of 735 K to offset its higher fuel reactivity than the iso-octane, such that the flames of both fuels can have a similar lift-off length. Forced laser ignition was introduced either before or after the natural autoignition timing of the fuels. The laser was focused at the jet axis 15 mm and 30 mm from the nozzle. High-speed schlieren imaging, heat release analysis and flame luminosity measurement were applied to the flames. The high-speed schlieren imaging was used to monitor the flame structure evolution of the natural ignition and LI cases. Due to laser ignition, the flame lift-off lengths decrease, with which the uncertainties in the lift-off distances reduce by more than 80 %. The laser-affected flame bases return back to the natural flame base locations. The uncertainties in the lift-off lengths also increase, as the flame stabilisation locations approach the natural lift-off distances. Under the test conditions of this work, the rates at which the iso-octane flames shift downstream are slower than in the n-heptane cases. The heat release rate profiles show high heat release from the flames following the LI events, before transitioning to lower steady values. The flame luminosity measurements indicate a strong correlation between the LI affected lift-off length and increased soot formation. The luminosity levels decrease as the flame base shifts downstream over time. The third part aims to investigate the underlying processes governing ignition and flame stabilisation in CI engine-relevant conditions. Primary reference fuels (PRFs), including PRF100 (neat iso-octane), PRF80 (a blend of 80 vol.% iso-octane and 20 vol.% n-heptane) and PRF0 (neat n-heptane), were tested to simulate changes in fuel ignition quality inside a quiescent steady environment with an ambient density of 22.8 kg/m3 and an O2 concentration of 15 vol. %. The ambient gas temperatures were controlled at 1150 K (PRF100), 1120 K (PRF80) and 900 K (PRF0), in order to adapt to the fuel reactivity so that a constant ignition delay of 1.15 ms can be achieved for all blends. This approach was employed in order to substantially reduce the effect of fuel-oxidiser mixing prior to ignition while highlighting the effect of fuel chemistry on the ignition process and flame evolution. Under the test conditions of this study, optical imaging reveals that the blends with higher iso-octane content exhibit a faster spreading of combustion after ignition and establish a steady lifted flame that is closer to the nozzle. Imaging by CH2O-PLIF indicates that blends with higher iso-octane content produce CH2O that is distributed across larger portions of the jet at an earlier timing when compared to neat n-heptane that shows a propagating first-stage ignition through the fuel jet. Supporting unsteady flamelet calculations are presented to investigate the effect of chemistry and turbulent mixing. The flamelet calculations agree qualitatively in several respects to the experiments, especially in the spatial and temporal trends for CH2O production and consumption. Synthesis of the flamelet and experimental results suggests that for the iso-octane-containing fuels, CH2O is formed via single-stage ignition reactions rather than exhibiting the typical two-stage ignition behaviour which is found in the pure n-heptane fuel case. Furthermore, the flamelet calculations suggest high-temperature ignition occurs first in lean mixtures in the iso-octane-containing fuel cases, but in rich mixtures for the PRF0 case. If autoignition is the mode of flame stabilisation, this provides an explanation for why the PRF100 and PRF80 cases stabilise further upstream, since lean mixtures have longer residence times, experience lower scalar dissipation rate, and maybe more likely to be exposed to a supporting peripheral reservoir of hot products, should one exist. Overall, this study provides insights into the roles of fuel chemistry and turbulent mixing on the ignition and combustion behaviour of PRFs under engine-relevant conditions.