As we make progress towards the era of fifth generation (5G) communication networks, energy efficiency (EE) becomes an important design criterion because it guarantees sustainable evolution. In this regard, the massive multiple-input multiple-output (MIMO) technology, where the base stations (BSs) are equipped with a large number of antennas so as to achieve multiple orders of spectral and energy efficiency gains, will be a key technology enabler for 5G. In this article, we present a comprehensive discussion on state-of-the-art techniques which further enhance the EE gains offered by massive MIMO (MM). We begin with an overview of MM systems and discuss how realistic power consumption models can be developed for these systems. Thereby, we discuss and identify few shortcomings of some of the most prominent EE-maximization techniques present in the current literature. Then, we discuss "hybrid MM systems" operating in a 5G architecture, where MM operates in conjunction with other potential technology enablers, such as millimetre wave, heterogenous networks, and energy harvesting networks. Multiple opportunities and challenges arise in such a 5G architecture because these technologies benefit mutually from each other and their coexistence introduces several new constraints on the design of energy-efficient systems. Despite clear evidence that hybrid MM systems can achieve significantly higher EE gains than conventional MM systems, several open research problems continue to roadblock system designers from fully harnessing the EE gains offered by hybrid MM systems. Our discussions lead to the conclusion that hybrid MM systems offer a sustainable evolution towards 5G networks and are therefore an important research topic for future work.