The electrical grid is undergoing a fundamental change with the introduction of smart grid technologies. In particular, power substations have been evolving toward more automated systems. Power substation communication networks evolved from infrastructures mostly formed by serial devices to Ethernet-based digital communications networks, accelerating with the introduction of the IEC 61850 set of standards. However, this evolution inherited the shortcomings of the traditional decentralized network management. This article explores the upcoming evolution of IEC 61850 to meet the groundbreaking programmable network technologies: software-defined networks (SDNs) and programmable data planes (PDPs). Here, we describe how recent proposals leverage SDNs to improve network management tasks such as topology discovery, multicast traffic management, and quality-of-service (QoS) provisioning, among others in IEC 61850-based systems. We also outline potential improvements to critical network management tasks in power substations using PDP features such as in-band network telemetry. Finally, we discuss different challenges in the management of the communication networks of smart power substations and addressing them with the implementation of programmable networks.