Neural recording systems are a central component of Brain-Machince Interfaces (BMIs). In most of these systems the emphasis is on faithful reproduction and transmission of the recorded signal to remote systems for further processing or data analysis. Here we follow an alternative approach: we propose a neural recording system that can be directly interfaced locally to neuromorphic spiking neural processing circuits for compressing the large amounts of data recorded, carrying out signal processing and neural computation to extract relevant information, and transmitting only the low-bandwidth outcome of the processing to remote computing or actuating modules. The fabricated system includes a low-noise amplifier, a delta-modulator analog-to-digital converter, and a low-power band-pass filter. The bio-amplifier has a programmable gain of 45-54 dB, with a Root Mean Squared (RMS) input-referred noise level of 2.1 μV, and consumes 90 μW . The band-pass filter and delta-modulator circuits include asynchronous handshaking interface logic compatible with event-based communication protocols. We describe the properties of the neural recording circuits, validating them with experimental measurements, and present system-level application examples, by interfacing these circuits to a reconfigurable neuromorphic processor comprising an array of spiking neurons with plastic and dynamic synapses. The pool of neurons within the neuromorphic processor was configured to implement a recurrent neural network, and to process the events generated by the neural recording system in order to carry out pattern recognition.