The measurement of newborns' brain hemodynamic activity has improved our understanding of early cognitive processes, in particular of language acquisition. In this paper, we describe two experimental protocols adapted to study neonates' speech-processing capacities using functional near-infrared spectroscopy (fNIRS): the block design and the familiarization-recognition design. We review some of their benefits and disadvantages, and refer to research issues that can be explored by means of these protocols. We also illustrate the use of the two experimental designs through representative fNIRS studies that reveal specific patterns of activation of the newborn brain during speech perception, learning of repetition structures, and word recognition.