An infinity harmonic function is a (viscosity) solution to the infinity Laplace equation, which is the Euler-Lagrange equation of absolute (or local) minimizers of super-norm of the gradient. The subject has received considerable interests very recently along with many basic questions that need to be understood. In this talk, I will first review some basic results of infinity harmonic functions. Then I will present the following theorem: Near any non-removable isolated singular point $x_0$, an infinity harmonic function $u$ has the following asymptotics:
$$u(x)=u(x_0)+c|x-x_0|+o(|x-x_0|).$$ In particular, $x_0$ is a local max or min point of $u$.