Sewall Wright's powerful metaphor of rugged adaptive landscapes has formed the basis for discussing evolution and speciation for more than 60 years. However, this metaphor with its emphasis on adaptive peaks and valleys is to a large degree a reflection of our three-dimensional experience. Both genotypes and phenotypes of biological organisms differ in numerous characteristics, and, thus, the dimension of `real' adaptive landscapes is much larger than three. Properties of multidimensional adaptive landscapes are very different from those of low dimension. Consequently, something that is seen as a theoretical challenge in a low-dimensional case might be a trivial problem in a multidimensional context and vice versa. In particular the problem of how a population crosses an adaptive valley on its way from one adaptive peak to another, which Wright attempted to solve with his shifting balance theory, may be non-existent. A new framework is emerging for deepening our understanding of evolution and speciation, which provides a plausible multidimensional alternative to the conventional view of rugged adaptive landscapes.