Fluorescence is a powerful and sensitive tool in biological detection, used widely for cellular imaging and in vitro molecular diagnostics. Over time, three prominent conventions have emerged in the design of fluorescent biosensors: a sensor is ideally specific for its target, only one fluorescence signal turns on or off in response to the target, and each target requires its own sensor and signal combination. These are conventions but not requirements, and sensors that break with one or more of these conventions can offer new capabilities and advantages. Here, we review "unconventional" fluorescent sensor configurations based on fluorescent dyes, proteins, and nanomaterials such as quantum dots and metal nanoclusters. These configurations include multifluorophore Förster resonance energy transfer (FRET) networks, temporal multiplexing, photonic logic, and cross-reactive arrays or "noses". The more complex but carefully engineered biorecognition and fluorescence signaling modalities in unconventional designs are richer in information, afford greater multiplexing capacity, and are potentially better suited to the analysis of complex biological samples, interactions, processes, and diseases. We conclude with a short perspective on the future of unconventional fluorescent sensors and encourage researchers to imagine sensing beyond the metaphorical light bulb and light switch combination.