  The Li\'enard equation is used in various applications. Therefore,
constructing general analytical solutions of this equation is an important
problem. Here we study connections between the Li\'enard equation and some
equations from the Painlev\'e--Gambier classification. We show that with the
help of such connections one can construct general analytical solutions of the
Li\'enard equation's subfamilies. In particular, we find three new integrable
families of the Li\'enard equation. We also propose and discuss an approach for
finding one--parameter families of closed--form analytical solutions of the
Li\'enard equation.
