It is well known that the space of modular forms is not stable under differentiation. This is why quasi-modular forms have been introduced. Also Drinfeld modular forms, that are the positive characteristic counterpart of classical modular forms, are not stable under differentiation. In 2008 V. Bosser and F. Pellarin introduced Drinfeld quasi-modular forms of level 1. In this talk we will present some new and recent advances on Drinfeld quasi-modular forms of higher level.