Deformable soft matter, such as liquid drops and bubbles, exhibits complex dynamics that play a crucial role in numerous natural phenomena and technological applications. This talk explores the fascinating world of hydrodynamic singularities in soft matter flows, focusing on sheets, drops and bubbles. Through a combination of experimental observations, high-fidelity direct numerical simulations, and theoretical analysis, we explore the multidimensional phase space and uncover novel insights into the physics governing these systems. Our investigation reveals how the interplay between surface tension, viscosity, and elasticity leads to the formation of singular Worthington jets during drop impacts and bursting bubbles. Furthermore, we elucidate the mechanisms behind sheet retraction. By bridging fundamental research with practical applications, our findings contribute to the development of water-repellent technologies, enhance our understanding of erosion processes, and provide insights into disease transmission through aerosols.