The brain is a complex system par excellence. Its intricate structure has become clearer recently, and it has been reported that it shares some properties common to complex networks, such as the small-world property, the presence of hubs, and assortative mixing, among others. These properties provide the brain with a robust architecture appropriate for efficient information transmission across different brain regions. Nevertheless, how these topological properties emerge in neural networks is still an open question. Moreover, in the last decade the observation of neuronal avalanches in neocortical circuits suggested the presence of self-organised criticality in neural systems. The occurrence of this kind of dynamics implies several benefits to neural computation. However, the mechanisms that give rise to critical behaviour in these systems, and how they interact with other neuronal processes such as synaptic plasticity are not fully understood. In this thesis, we study self-organised criticality and neural systems in the context of complex networks. Our work differs from other similar approaches by stressing the importance of analysing the influence of hubs, high clustering coefficients, and synaptic plasticity into the collective dynamics of the system. Additionally, we introduce a metric that we call node success to assess the effectiveness of a spike in terms of its capacity to trigger cascading behaviour. We present a synaptic plasticity rule based on this metric, which enables the system to reach the critical state of its collective dynamics without the need to fine-tune any control parameter. Our results suggest that retro-synaptic signals could be responsible for the emergence of self-organised criticality in brain networks. Furthermore, based on the measure of node success, we find what kind of topology allows nodes to be more successful at triggering cascades of activity. Our study comprises four different scenarios: i) static synapses, ii) dynamic synapses under spike-timing-dependent plasticity (STDP), iii) dynamic synapses under node-success-driven plasticity (NSDP), and iv) dynamic synapses under both NSDP and STDP mechanisms. We observe that small-world structures emerge when critical dynamics are combined with STDP mechanisms in a particular type of topology. Moreover, we go beyond simple spike pairs of STDP, and implement spike triplets to assess their influence on the dynamics of the system. To the best of our knowledge this is the first study that implements this version of STDP in the context of critical dynamics in complex networks.