Let $E: y^2=x^3+Ax+B$ be an elliptic curve over $\mathbb{Q}$. For each prime $p$ where $E$ has good reduction, let
\[
a_p := p+1-|E(\mathbb{F}_p)|
\] be the trace of Frobenius. A theorem of Hasse implies that the normalized trace $x_p:=a_p/\sqrt{p}$ is a real number in the interval $[-2,2]$. Surprisingly, as $p\to \infty$, these $x_p$ demonstrate a uniform distribution with respect to a certain measure. This is known as the Sato-Tate Conjecture and is now a theorem due to Richard Taylor and others. In this talk, I will introduce the Sato-Tate Groups for general abelian varieties over number fields which are compact subgroups of $USp(2g)$ lurking behind the scene of which the push-forward Haar measure conjecturally give rise to such uniform distributions. Hopefully I will be able to show some distribution diagrams by the end of the talk if time allows.