What makes the digits 645751311064590590501615753639260425710 and 1010100101010011111111010100111010010111 so special? These digits look as if they were chosen at random, yet they are entirely deterministic (take the fractional part of the square root of 7). In this talk, I will explore the theory of quasi-randomness, which characterizes ``random-like" sequences, graphs, sets, and many other objects. In particular, I will present a theory of quasi-randomness for Boolean functions and show how random Boolean functions lead to a very challenging open problem: the Inverse Theory of the Gowers Norms.