abstract: Drinfeld modular schemes were introduced by Drinfeld in order to prove the Langlands reciprocity of the function field analogue. Compactifying these moduli spaces is one of key steps for realizing the Langlands correpsondence in their l-adic cohomologies. Drinfeld constructed the compactification for rank 2 moduli spaces. Higher rank moduli spaces were constructed by Kapranov, Gekeler and Pink by different methods. In this talk we shall discuss the arithmetic Satake compacfication of Drinfeld moduli schemes of any rank following Pink's approach. Applications to algebraic Drinfeld modular forms are addressed. This is joint work with Urs Hartl.