This report summarises the lectures presented by Dr Draga Pihler-Puzović, who provided an introductory overview of Saffman-Taylor instabilities in elastic Hele-Shaw cells. By replacing the top plate in a Hele-Shaw cell with a thin elastic sheet, the formation of viscous fingers may be suppressed or trigger new instabilities due to the existing fluid-structure interactions. The morphology of the resultant viscous fingers depends highly on the taper near the air-fluid interface. Finally, the propagation of air fingers in bifurcation is addressed with an interesting focus on clinical applications for airway reopening.