The RNA helicase eIF4A plays a key role in unwinding of mRNA and scanning during translation initiation. Free eIF4A is a poor helicase and requires the accessory proteins eIF4G and eIF4H. However, the structure of the helicase complex and the mechanisms of stimulation of eIF4A activity have remained elusive. Here we report the topology of the eIF4A/4G/4H helicase complex, which is built from multiple experimentally observed domain-domain contacts. Remarkably, some of the interactions are continuously rearranged during the ATP binding/hydrolysis cycle of the helicase. We show that the accessory proteins modulate the affinity of eIF4A for ATP by interacting simultaneously with both helicase domains and promoting either the closed, ATP-bound conformation or the open, nucleotide-free conformation. The topology of the complex and the spatial arrangement of the RNA-binding surfaces offer insights into their roles in stimulation of helicase activity and the mechanisms of mRNA unwinding and scanning.