Polymer nanomaterials have been of scientific and industrial interest due to their applications in filtration, energy storage, and biomedical engineering. The electrospinning and electrospray processes can produce functional nanofibers and nano-coatings respectively. In these processes, the liquid solution is ejected out of a nozzle and the liquid jets or droplets travel towards the collector under an electric field. There have been numerous experimental studies on these processes where the behavior of different viscoelastic polymer systems at various process conditions are studied. The theoretical studies are limited due to the mathematical complexity of the polymer rheology and also the non-linear effects of the process. In this thesis, a discretized model for spinning and spraying process is discussed. In the model, the polymer jet is considered to be made up of discrete beads attached with massless springs. The jet trajectory is obtained by following a Lagrangian approach and applying conservation of mass and momentum equations to each bead. In addition, the whipping and axisymmetric instabilities on electrically driven jets are also discussed. In the electrospinning process, the whipping instability causes the jet to undergo non-axisymmetric motion and leads to uncontrolled deposition of the jet on the collector. To reduce the whipping motion of the fiber, the spinning solution is electrospun in a liquid medium and this modified system is called as the immersed electrospinning system. This modified system allows the electrically driven jets to 2D or 3D print on the substrate and form ordered fiber mats. In our printing approach, the nozzle system is stationary, and the fiber is electrically maneuvered for printing on the substrate. However, in this setup, there is no proper contact between the printing jet and the substrate to form 3D structures. Therefore, we studied the motionless printing method in electrohydrodynamic jet printing and melt electrospinning. In these two setups, first, we studied the onset position of whipping instability at different applied voltage conditions to obtain controlled deposition. Later, for the melt electrospinning setup, we studied the formation of 3D square pattern with motionless printing approach. The axisymmetric instability is responsible for the modulations in the radius of the polymer jet. In the presence of an electric field, the growth rate of the instability increases, and the jet breaks up to form droplets. The electrically driven droplets electrosprays and forms a coating on the collector. When coaxial air flow is applied to the viscoelastic polymer jets in the electrospray process, it is called as the air controlled electrospray process. The comparison of the droplet size distribution from simulations and experiments for the cases: i) air spray, ii) electrospray and iii) air controlled electrospray is studied. The three spray processes are used to coat cathodes in lithium sulfur batteries and the electrochemical performance of the batteries are compared. In addition, the effect of air flow on the surface morphology of the coating on the substrate is also discussed. Finally, the discretized model is used to study an industrial scale rotary bell spray process that is used in the automobile industry to coat the car body.