We present here a learning system using the iCub humanoid robot and the SpiNNaker neuromorphic chip to solve the real-world task of object-specific attention. Integrating spiking neural networks with robots introduces considerable complexity for questionable benefit if the objective is simply task performance. But, we suggest, in a cognitive robotics context, where the goal is understanding how to compute, such an approach may yield useful insights to neural architecture as well as learned behavior, especially if dedicated neural hardware is available. Recent advances in cognitive robotics and neuromorphic processing now make such systems possible. Using a scalable, structured, modular approach, we build a spiking neural network where the effects and impact of learning can be predicted and tested, and the network can be scaled or extended to new tasks automatically. We introduce several enhancements to a basic network and show how they can be used to direct performance toward behaviorally relevant goals. Results show that using a simple classical spike-timing-dependent plasticity (STDP) rule on selected connections, we can get the robot (and network) to progress from poor task-specific performance to good performance. Behaviorally relevant STDP appears to contribute strongly to positive learning: "do this" but less to negative learning: "don't do that." In addition, we observe that the effect of structural enhancements tends to be cumulative. The overall system suggests that it is by being able to exploit combinations of effects, rather than any one effect or property in isolation, that spiking networks can achieve compelling, task-relevant behavior.