It is widely recognised that improving the visibility and controllability of distributed energy resources (DERs) within electricity distribution networks will have significant benefits, particularly for the management of low-voltage (LV) and medium-voltage (MV) networks. Much work within the electricity distribution industry is currently focused on improving the visibility of DERs on LV networks. From a control-theoretic perspective, this enables closing the loop between the DER and the control room and enables a shift towards utilising data-driven model-based control strategies for DERs. The result is a system-wide performance that is closer to the theoretical optimal. In the Australian context, several jurisdictions are trialling techniques such as dynamic operating envelopes to enhance DER hosting capacity, using IEEE 2030.5-based architectures, with the implementation of distributed energy resource management (DERMS) systems at the enterprise level still quite limited. While there is significant activity focused on DER behaviour and control techniques by way of inverter grid codes and standards, the core issue of interoperability with distribution management systems (DMSs), market operators or participants, electric vehicles (EVs) or other DERs is still a work in progress. Importantly, this is also an impediment to realising distributed architectures for DER control in the grid. The unique characteristics of Australian distribution networks highlights several challenging problems for DER control and management. The objective of this paper is to provide a broad overview of DER control and management strategies in the Australian context, with an application focus on DER control in distribution network management.