The development of CCG and Lambek style typelogical grammars in the 1980s initially followed separate courses. More recently, there are signs of convergence. An important factor has been the introduction of the typelogical technique of multimodal control to fine-tune the applicability of the CCG combinatory schemata (Baldridge 2002, Kruijff and Baldridge 2003).  Multimodal typelogical grammar, from this perspective, plays the role of the underlying general logic which one uses to establish the validity of the CCG combinatory schemata, whereas the particular choice of primitive combinators is motivated by computational efficiency considerations (Hoyt and Baldridge 2008). In terms of generative capacity, CCG is a member of the mildly context sensitive family of grammar formalisms. Polynomial parsability is obtained by imposing a bound on the functional composition schemata.