In the first part of this article, the author presents his joint result with J. Colpaert on the classification of closed affine curves of finite type: The only closed affine curves of \(k\)-type, for any natural number \(k\), are the closed curves \(\gamma\) which lie fully in the affine \(2k\)- space \(A^{2k}\) and which are affinely equivalent to a closed \(W\)-curve of \(\text{rank }2k\) in a Euclidean \(2k\)-space \(E^{2k}\); in particular, these curves lie mass-symmetrically on an ellipsoid. Two immediate consequences: The ellipses are the only closed affine curves of finite type in the plane \(A^ 2\) and there exists no closed affine curve of finite type which lies fully in \(A^ 3\). In the second part the author presents his joint results with the reviewer, F. Dillen and L. Vrancken on submanifolds of restricted type. The details of the second part will appear in [\textit{B.-Y. Chen}, \textit{F. Dillen}, \textit{L. Verstraelen} and \textit{L. Vrancken}, Submanifolds of restricted type, J. Geom. (to appear)].