Ink-jet deposition is an emerging technology that provides a more efficient, economic, scalable method of manufacturing than other traditional additive techniques by laying down droplets layer by layer to build up 3-D objects. The focus of this thesis is to investigate the material interface evolution during the droplet deposition process, which holds the key to understanding the material joining process. Droplet deposition is a complicated process and can be broken down into droplet impingement dynamics and droplet hardening. This research focuses on the study of the interface dynamics of droplet impingement. In order to study the interface dynamics, a novel metric is developed to quantify the evolving geometry of the droplet interface in both 2-D and 3-D for single and multiple droplets respectively, by measuring the similarity between the evolving droplet geometry and a desired shape. With the developed shape metric, the underlying physics of the interface evolution for single droplet impingement are examined with simulations using an experimentally validated numerical model. Results show that the Weber number determines the best achievable shape and its timing during the droplet impingement when Ohnesorge number is smaller than 1, while the Reynolds number is the determining factor when Ohnesorge number is larger than 1. A regime map is constructed with the results and an empirical splash criterion to guide the choice of process parameters for given fluid properties in order to achieve the best shape without splash for single droplet impingement. In order to study the interface dynamics for multiple droplet interaction, which is computationally prohibitive for commercial software packages, an efficient numerical model is developed based on the Lattice Boltzmann (LB) method. A new LB formulation equivalent to the phase-field model is developed with consistent boundary conditions through a multiscale analysis. The numerical model is validated by comparing its simulation results with that of commercial software COMSOL and experimental data. Results show our LB model not only has significant improvement of computational speed over COMSOL but is also more accurate. Finally, the developed numerical solver is used to study the interface evolution of multiple droplet interaction with the aid of the 3-D shape metric proposed before. Simulations are performed on a wide range of impingement conditions for two-droplet, a-line-of-droplet, and an-array-of-droplet interactions. The underlying physics of the interface coalescence and breakup coupling with the impingement dynamics are examined. For line-droplet interaction, the strategy for achieving the equilibrium shape in the shortest time is studied. An important issue is discovered for array-droplet interaction, which is the air bubble formation during the droplet interaction. The mechanism for the air bubble formation is investigated and the strategy to avoid this undesirable effect is also suggested. This thesis has largely reduced the gap between basic science of studying droplet impingement dynamics and engineering application in inkjet deposition and provided preliminary insights on the material joining process for additive manufacturing.