We will discuss various Hecke operators on modular forms for $SL(2, \mathbb{Z})$. A standard result states that all Hecke operators, $T(p^a)$, can be generated by a single Hecke operator, $T(p)$, making it the only Hecke operator of interest. We will then discuss Hecke operators on Siegel modular forms for $Sp(4, \mathbb{Z})$. There is a similar result in this case which states that every Hecke operator, $T(p^a)$, can be generated by Hecke operators $T(p)$ and $T(p^2)$. We will discuss how these operators can be expressed in terms of Fourier expansions.