The toxicity, climate impact, as well as the physical and chemical properties of ultra-fine soot particles emitted from combustion systems are strongly dependent on their size and morphology. Research attention has been paid in the last three decades to developing more accurate and capable methods to model soot particle coagulation in the presence of inception, surface growth, and oxidation, to predict particle size distribution as well as the detailed aggregate morphology of soot. While soot particle concentrations in hydrocarbon flames are primarily governed by soot kinetics, the morphology of soot particles is controlled by both soot kinetics and particle dynamics. Flame-generated soot particles are fractal aggregates formed by polydisperse and nearly spherical primary particles with a certain degree of overlapping. The properties of fractal aggregates, nanoparticle coagulation, and soot formation chemistry all play important roles in soot formation. This article reviews all these aspects but the focus is on recent progress in macro- and meso-scale modeling of soot particle aggregation in laminar sooting flames to avoid the complexities of turbulence. The reviewed macro-scale methods based on the population balance equation include the commonly used sectional methods and methods of moments. The main features of three recently developed state-of-the-art meso-scale methods, namely the event-driven Discrete Element Method, Monte Carlo Aggregation Code, and detailed stochastic population balance model are reviewed. To highlight the complexities of modeling the particle size distribution and detailed particle morphology without and with surface growth, numerical simulations of three test cases were conducted using the event-driven Discrete Element Method, the Monte Carlo Aggregation Code, and the two macro-scale methods. A detailed analysis of the results was presented to understand how different treatments of particle coagulation and surface growth in the two meso-scale methods affect the predicted particle size and morphology. The remaining challenges in modeling detailed soot particle morphology are outlined.