This paper describes and discusses recent theories of conceptual combination made up of a Modifier (adjective or noun) and a head noun. If all models assume that the interpretation of a conceptual combination implies that a relation is established between the Modifier and the Head Noun to create a new concept, they differ by the kind of link and process implied to create this connexion between the two concepts. The first category of models (Gagne et Shoben, 1997) assume that the world knwledge concerning the relations that are typically used with the Modifier concept is brought to bear immediately as part of the interpretation process (Gagne, 2000, 2001). The second category puts forward the notion of schema with its structural and functional properties to determine the meaning of combined concepts (Smith, Osherson, Rips and Keane, 1988; Murphy, 1988). Among this category, the ``Dual Process'' model (Wisniewski (1997, 2001) and the ``Constraint-Guided Conceptual Combination Model'' (Costello et Keane, 2000, 2001) first try to take into account the different types of interpretation: relational, transfert of property and hybrid, and secondly to describe how and when world knowledge influences conceptual combination.