The 2-dimensional dragon curves obtained from paper-folding sequences have been studied in several papers [see \textit{Davis} and \textit{Knuth}, J. Recreat. Math. 3, 61-81 and 133-149 (1970); \textit{F. M. Dekking}, \textit{M. Mendès France} and \textit{A. J. van der Poorten}, Math. Intell. 4, 130- 138, 173-195 (1985; Zbl 0493.10001, Zbl 0493.10002); \textit{M. Mendès France} and \textit{A. J. van der Poorten}, Bull. Austr. Math. Soc. 24, 123- 131 (1981; Zbl 0451.10018)]. In the first of these papers, Davis and Knuth ask whether there are 3-D ``dragon curves'' which have both aesthetic and interesting properties. The paper under review gives an answer to this question by studying the sequences obtained from bending wires. The authors study these sequences from the point of view of binary expansion of integers, of finite automata and of continued fractions. One very surprising result is that the curves traced out in 3-D are very often bounded curves, which is in sharp contrast to the 2-D case where the curves are not self-intersecting. Let us finally say that the related ``handkerchief-folding'' sequences, and the ``p-paperfolding'' sequences have been recently studied, respectively, by \textit{O. Salon} [Sémin. Théor. Nombres, Univ. Bordeaux I 1986/1987, Exp. No.4 (1987; Zbl 0653.10049)] and by \textit{D. Razafy Andriamampianina} [Ann. Fac. Sci. Toulouse (to appear); see the following preview Zbl 0663.10057)], and that the paper-folding regular polygons [see for instance \textit{J. Froemke} and \textit{J. W. Grossman}, Am. Math. Mon. 95, No.4, 289-307 (1988; Zbl 0651.10002)] seem to have no relationship with the above sequences.