Biological neuronal cultures offer the unique opportunity to study the emergent behaviour of networks comprised of a large number of neurones within a controlled environment. Such neurones typically develop random interconnections, yet exhibit certain spontaneous properties reflective of their original function. In vitro cultures are maintained and ob- served using specialised multi-electrode arrays (MEAs), which record their activity in the form of extracellular voltages called spikes and are able to concurrently stimulate them at multiple locations via electrical impulses. Currently, cultures are often being used as the primary controllers in biological-machine hybrids. One of the most intriguing questions however is how to best capture the com- plex interactions of neuronal ensembles and their evolution in time, which would lead to a better understanding of mechanisms of learning and memory. Their spatiotemporal dynamics need to be taken into consideration in any hybrid closed-loop system in order to describe and predict its state at any point in time. To this extent, first the use of temporal coding schemes was examined within spon- taneous and stimulated activity and confirmed certain robust patterns of behaviour. Sub- sequently, both spatial and temporal dynamics of cultures were studied with the use of hidden Markov models (HMMs). Relevant research has demonstrated the capabilities of HMMs in an in vivo context, but their applicability in vitro is not yet widely explored. Two types of models were proposed and important aspects of their framework were anal- ysed for use with multi-channel neuronal recordings. The models were used to analysed a range of spontaneous activity and evoked responses and uncovered robust, repeated dynamic patterns. This led to an important question: how do these dynamic states relate between different conditions? Spectral clustering techniques were implemented to answer this question and study the extent of similarities between different culture behaviours. Future directions of this work anticipate the application of HMMs to improve real- time systems which utilise neuronal cultures as the controlling brains of artificial robotic agents, with further implications for neuroprosthetics and brain-machine interfaces.