The radiation effects in SOI structures are discussed in the context of the device miniaturization. We review radiation data accumulated in the recent years and point out new directions of research. The properties of standard and innovative SOI wafers with buried alumina are presented. The scaling of partially depleted SOI MOSFETs results in new mechanisms, such as gate-induced floating body, which combine with more classical effects. On the other hand, fully depleted transistors with ultra thin body are prone to giant coupling effects. The operation principles of transistors with double, triple or quadruple gates are briefly addressed. It is demonstrated that the volume conduction, enabled in multiple-gate MOSFETs, exhibits superior resistance to radiations.