Up until around ten years ago, third language acquisition (L3A) research was generally subsumed under the umbrella term of second language acquisition (L2A). In this short space of time, however, L3A has established itself as an independent strand of linguistic research, providing an invaluable source of information into language and language acquisition. This paper emphasises the crucial differences between L2A and L3A. It provides a snapshot of the current state of cognitive research into L3A, discussing studies in the domains of morphology, syntax, phonology and lexicon. Recently proposed (specific L3) generative models are discussed, such as Cumulative Enhancement Model (Flynn, Foley & Vinnitskaya, 2004), L2 Status Factor (Bardel & Falk, 2007) and Typological Primacy Model (Rothman, 2011) together with an alternative proposal (Contextual Complexity Hypothesis, Hawkins & Casillas, 2007). Finally this paper highlights the gaps in our knowledge and the direction for future research in this fast-growing area of research.