Light verb constructions (LVC) are complex predicates that are present in many languages. They belong to the Multiword Expression category known as verbal MWEs and has the canonical form of verb+noun. Examples of LVCs include give help, make decisions, and take walks. LVC identification is essential for many natural language processing (NLP) applications such as machine translation, sentiment analysis, and information extraction. However, the task of LVC identification is challenging due to its characteristics such as variability, discontinuity, and ambiguity. This paper presents a review of recent work, discusses the gaps that still exist, and proposes some future work that may contribute significant progress in LVC identification.