Formal schemes are, for admissible rings, the analogues of schemes for ordinary rings. Formal schemes were originally introduced alongside ordinary schemes in EGA, largely as tools for understanding the latter. While they served well in such applications, more recent developments, particularly in rigid analytic geometry, have motivated a study of formal schemes in their own right. In this talk I will discuss some vanishing theorems for formal schemes as work towards establishing a minimal model program for (some suitable class of) them.