In this talk I will give a brief history about a curious one-dimensional compact connected metric space called the pseudo-arc. Then I will review our recent work on genericity of interval Lebesgue measure-preserving functions on the interval and circle and connect this to the pseudo-arc. This talk is based on a joint work with Jozef Bobok (ÈVUT Prague), Piotr Oprocha (AGH Krakow & IRAFM Ostrava) and Serge Troubetzkoy (Aix-Marseille).