In this paper, we will first introduce the notions of systematicity and combinatorial productivity and we will argue that these notions are essential for human cognition and probably for every agent that needs to be able to deal with novel, unexpected situations in a complex environment. Agents that use compositional representations are faced with the so-called binding problem and the question of how to create neural network architectures that can deal with it is essential for understanding higher level cognition. Moreover, an architecture that can solve this problem is likely to scale better with problem size than other neural network architectures. Then, we will discuss object-based attention. The influence of spatial attention is well known, but there is solid evidence for object-based attention as well. We will discuss experiments that demonstrate object-based attention and will discuss a model that can explain the data of these experiments very well. The model strongly suggests that this mode of attention provides a neural basis for parallel search. Next, we will show a model for binding in visual cortex. This model is based on a so-called neural blackboard architecture, where higher cortical areas act as processors, specialized for specific features of a visual stimulus, and lower visual areas act as a blackboard for communication between these processors. This implies that lower visual areas are involved in more than bottom-up visual processing, something which already was apparent from the large number of recurrent connections from higher to lower visual areas. This model identifies a specific role for these feedback connections. Finally, we will discuss the experimental evidence that exists for this architecture.