This paper overviews the design and implementation of three neuromorphic integrated circuits developed for the COLAMN ("Novel Computing Architecture for Cognitive Systems based on the Laminar Microcircuitry of the Neocortex") project. The circuits are implemented in a standard 0.35 μm CMOS technology and include spiking and bursting neuron models, and synapses with short-term (facilitating/depressing) and long-term (STDP and dopamine-modulated STDP) dynamics. They enable execution of complex nonlinear models in accelerated-time, as compared with biology, and with low power consumption. The neural dynamics are implemented using analogue circuit techniques, with digital asynchronous event-based input and output. The circuits provide configurable hardware blocks that can be used to simulate a variety of neural networks. The paper presents experimental results obtained from the fabricated devices, and discusses the advantages and disadvantages of the analogue circuit approach to computational neural modelling.