Wireless sensor networks (WSNs) are a widely used solution for monitoring-oriented applications (e.g., water quality on watersheds, pollution monitoring in cities). These kinds of applications are characterized by the necessity of two data-reporting modes: time-driven and event-driven. The former is used mainly for continually supervising an area and the latter for event detection and tracking. By switching between both modes, a WSN can improve its energy efficiency and event-reporting latency, compared to single data-reporting schemes. We refer to those WSNs, where both data-reporting modes are required simultaneously, as multimodal wireless sensor networks (M2WSNs). In this paper, we present, from an energy-efficiency perspective, a review of switching mechanisms for M2WSNs. Besides, we explore two sophisticated techniques required in M2WSNs for further energy saving and event-reporting latency reduction purposes: duty-cycling and wake-up radio. We highlight future directions concerning switching and network management techniques for M2WSNs. To our knowledge, this review is first of its kind.