Syllables play an important role in speech synthesis and recognition. We present several different approaches to the syllabification of phonemes. We investigate approaches based on linguistic theories of syllabification, as well as a discriminative learning technique that combines Support Vector Machine and Hidden Markov Model technologies. Our experiments on English, Dutch and German demonstrate that our transparent implementation of the sonority sequencing principle is more accurate than previous implementations, and that our language-independent SVM-based approach advances the current state-of-the-art, achieving word accuracy of over 98% in English and 99% in German and Dutch.