In this paper, we present two novel perspectives on the function of the left inferior frontal gyrus (LIFG). First, a structured sequence processing perspective facilitates the search for functional segregation within the LIFG and provides a way to express common aspects across cognitive domains including language, music and action. Converging evidence from functional magnetic resonance imaging and transcranial magnetic stimulation studies suggests that the LIFG is engaged in sequential processing in artificial grammar learning, independently of particular stimulus features of the elements (whether letters, syllables or shapes are used to build up sequences). The LIFG has been repeatedly linked to processing of artificial grammars across all different grammars tested, whether they include non-adjacent dependencies or mere adjacent dependencies. Second, we apply the sequence processing perspective to understand how the functional segregation of semantics, syntax and phonology in the LIFG can be integrated in the general organization of the lateral prefrontal cortex (PFC). Recently, it was proposed that the functional organization of the lateral PFC follows a rostro-caudal gradient, such that more abstract processing in cognitive control is subserved by more rostral regions of the lateral PFC. We explore the literature from the viewpoint that functional segregation within the LIFG can be embedded in a general rostro-caudal abstraction gradient in the lateral PFC. If the lateral PFC follows a rostro-caudal abstraction gradient, then this predicts that the LIFG follows the same principles, but this prediction has not yet been tested or explored in the LIFG literature. Integration might provide further insights into the functional architecture of the LIFG and the lateral PFC.