We discuss questions and some results related to quantum tunneling, aiming towards a better understanding of bubble nucleation in cosmological phase transitions. First, we describe attempts to estimate the shape of phase transition bubbles in field theory, at and after nucleation, commenting on the single-bubble source of gravitational waves in early universe transitions. Then, to better understand the physics behind the standard imaginary-time semiclassical approximation, we study tunneling in 1D quantum mechanics. Using the path integral in real time, where tunneling solutions of the equations of motion live in the complex plane, we unravel the analytic structure of the action and show how the imaginary-time bounce saddle point emerges at the lowest order in a 1/t expansion.