It has been known for almost a hundred years that most polynomials with integral coefficients are irreducible. For a few dozen of years, people have been interested whether the same holds when one considers sparse families of polynomials — most notably, polynomials with plus-minus 1 coefficients. In particular, some guy on the street conjectures that the probability for a random plus-minus 1 coefficient polynomial to be irreducible tends to 1 as the degree tends to infinity. In this talk, I will discuss these types of problems, some approaches to attack them, and I will present some new results toward it, joint with Gady Kozma.