The aim of this project is to enable robots to recognise objects and object categories by combining vision and touch. In this thesis, a novel inexpensive tactile sensor design is presented, together with a complete, probabilistic sensor-fusion model. The potential of the model is demonstrated in four areas: (i) Shape Recognition, here the sensor outperforms its most similar rival, (ii) Single-touch Object Recognition, where state-of-the-art results are produced, (iii) Visuo-tactile object recognition, demonstrating the benefits of multi-sensory object representations, and (iv) Object Classification, which has not been reported in the literature to date. Both the sensor design and the novel database were made available. Tactile data collection is performed by a robot. An extensive analysis of data encodings, data processing, and classification methods is presented. The conclusions reached are: (i) the inexpensive tactile sensor can be used for basic shape and object recognition, (ii) object recognition combining vision and touch in a probabilistic manner provides an improvement in accuracy over either modality alone, (iii) when both vision and touch perform poorly independently, the sensor-fusion model proposed provides faster learning, i.e. fewer training samples are required to achieve similar accuracy, and (iv) such a sensor-fusion model is more accurate than either modality alone when attempting to classify unseen objects, as well as when attempting to recognise individual objects from amongst similar other objects of the same class. (v) The preliminary potential is identified for real-life applications: underwater object classification. (vi) The sensor fusion model providesimprovements in classification even for award-winning deep-learning basedcomputer vision models.