The properties of very-high-spin states at the yrast line are addressed. Three different but related topics are discussed: the status of yrast isomers (mainly in the A approx. 150 region); the nuclear shape along the yrast line; and the feeding of the yrast states as a function of spin. A recurrent theme is the response of the core to the polarizing effects of a successively increasing number of valence particles and how the investigation of very-high-spin states bears on this problem. 10 figures, 1 table. (RWR)