Neuromorphic computing is a wide research field aimed to the realization of brain-inspired hardware, apt to tackle computation of unstructured data more efficiently than currently done with standard computational units. Oscillatory neural networks are known for their associative memory capability, which enables to retrieve the information stored in the system from noisy or incomplete data. The development of phase-transition materials such as vanadiumdioxide (VO2) allows to design compact relaxation oscillator units which can be coupled in frequency and phase to realize an oscillatory neural network in hardware. In this thesis, we investigate the oscillatory neural network technology from the realization of the basic oscillator components with VO2 to the exploitation of the coupled oscillators as analog filters in convolutional neural networks applications. VO2 phase-transition devices are realized in a CMOS compatible process in two geometries, a planar and a crossbar configuration. The impact of the polycrystallinity of the VO2 film on the insulator-to-metal transition of the device is analyzed; through the contacting of a single grain we demonstrate the realization of a VO2 device with a single, sharp phase transition. The VO2 devices are connected in circuits to build networks of coupled oscillators. Through coupling with resistive and capacitive elements, experimental demonstrations of a 4-VO2 coupled oscillator network is shown. The network encodes the input and output information in the relative phase of the oscillators. The associative memory capability of the system is used to extract features from hand-written digits. By expanding the network to a 3×3 coupled oscillator system, we demonstrate in simulations how an oscillatory neural network can replace up to five digital filters in a convolutional neural network, retaining the same image processing capabilities.