Collective neural phenomena, such as oscillations and avalanches, are high-level neural signatures observed in aggregated spiking neuronal activity which have been consistently associated with a range of cognitive functions. However, it is often hard to elucidate whether such phenomena are mere epiphenomena or have causal or informational relevance. Experimental interventions that selectively disrupt the population-level activity are difficult to design and statistical measures to test their causal power struggle with the high-dimensionality of neuronal activity and the presence of widespread redundancy among neurons. In this work, we investigate this question by leveraging recent information-theoretic tools to identify emergent phenomena between relevant scales of neural activity. For this, we propose a computational framework combining information-theoretic and network science principles, which we use to investigate emergence in both in-vivo datasets and in-silico simulations. Our approach enables characterisation of emergence phenomena, identifies the relevant scales at which they take place, and elucidates the network-level mechanisms that underpin them. Results show that in-vivo neuronal oscillations show substantial emergent behaviour for smaller prediction delays, while critical avalanches exhibit their emergent nature at larger timescales. These results are supported by in-silico simulations, which show that the emergent signature of oscillations is facilitated by the network structure and interneuronal time-delays. Simulating a multi-assembly network tuned through a critical transition further reveals that oscillations and critical avalanches are both emergent but differ in kind, downward causation being exclusive to the oscillatory regime while critical dynamics come closest to being causally decoupled from their parts. Overall, these results highlight the role of network-level interactions between groups of neuronal assemblies as the key driver of emergent population activity in the brain.