The breakup of liquid filaments plays a crucial role in both industrial processes (such as inkjet printing and spraying) and biomedical contexts, particularly in the airborne transmission of pathogens via saliva droplets generated during coughing, sneezing or speech. In this latter case, the droplets emitted carry viruses and thus represent a key vector for the transmission of diseases. To better assess and mitigate this risk, it is essential to understand how these droplets are formed in the first place. Their origin lies in the deformation and breakup of thin liquid filaments of saliva, stretched between the lips and disrupted by airflow during speech. This thesis investigates the dynamics of uniaxially stretched liquid filaments as they thin and break under the combined influence of viscous, inertial, and capillary forces, as well as under a controlled perpendicular airflow. In the first part, we examine how purely viscous filaments stretch in an original experimental setup designed to reproduce violent extensions, and how this thinning process is modified by airflow. We then focus on the filament shape under perpendicular airflow. Using a quasistatic approximation (neglecting inertia), we model the geometry with either slender-body viscous friction (low Reynolds number) or aerodynamic drag (Taylor model, high Reynolds number), and from these descriptions we compute the internal tension within the filament by simply fitting the shape of deformed filament in order to compare it to the inner viscous tension. Numerical simulations further confirm the validity of this quasistatic framework. The aim of the comparisons of tension is to validate one of the model and to have a quantitative way to study filament behaviour. These approaches are extended to viscoelastic fluids, in particular human saliva, showing that filament geometries can still be quantitatively characterized. From these measurements, it becomes possible to define an effective Ohnesorge number for saliva, allowing comparison with simpler Newtonian systems. The second part of the work addresses filament breakup and the variety of modes through which they destabilize and fragment, depending on viscosity, initial volume, and airflow conditions. We demonstrate that airflow can either accelerate or delay rupture, and even modify the breakup mechanism itself. Finally, we investigate model viscoelastic fluids (wormlike micelles) and saliva to show how elasticity influences thinning and breakup. These experiments reveal new behaviours, such as delayed rupture, extended lifetimes, and the appearance of instabilities along the filament. The main findings are: (i) the quasistatic model is reliable during pure deformation, between the end of bead extension and the onset of non-uniformities, but breaks down when drainage and inertia become significant; (ii) viscosity strongly stabilizes filaments at low Ohnesorge numbers, whereas airflow inertia promotes deformation and shifts breakup regimes; (iii) salivary elasticity enables extreme stretching and delays rupture over long timescales. Limitations remain: the study focuses mainly on glycerol as a model fluid, with fewer experiments on saliva and micelles, and no quantification of droplet number and size after breakup. Nevertheless, these results open the way to a more comprehensive understanding of complex biological fluids and their atomization, ultimately linking laboratory findings to the deformation and fragmentation of saliva filaments in the mouth and respiratory tract.