This paper specifies the main features of connectionist and brain-like connectionist models; argues for the need for, and usefulness of, appropriate successively larger brainlike structures; and examines parallel-hierarchical Recognition Cone models of perception from this perspective, as examples of networks exploiting such structures (e.g. local receptive fields, global convergence-divergence). The anatomy, physiology, behavior, and development of the visual system are briefly summarized to motivate the architecture of brain-structured networks for perceptual recognition. Results are presented from simulations of carefully pre-designed Recognition Cone structures that perceive objects (e.g. houses) in digitized photographs. A framework for perceptual learning is introduced, including mechanisms for generation learning, i.e. the growth of new links and possibly, nodes, subject to brain-like topological constraints. The information processing transforms discovered through feedback-guided generation are fine-tuned by feedback-guided reweighting of links. Some preliminary results are presented of brain-structured networks that learn to recognize simple objects (e.g. letters of the alphabet, cups, apples, bananas) through generation and reweighting of transforms. These show large improvements over networks that either lack brain-like structure or/and learn by reweighting of links alone. It is concluded that brain-like structures and generation learning can significantly increase the power of connectionist models.