In this talk, we are mainly concerned with the  \mu-type Camassa-Holm equations. First, we review the known results on the  \mu-type Camassa-Holm equations. Integrable properties and geometric aspects will be discussed. Second, we study the higher-order  \mu-type Camassa- Holm equations. New properties of those kind of equations will be explored. Finally, some open questions related to this talk will be addressed.