Fractional quantum Hall states exhibit many fascinating aspects of quantum many-body physics in an experimentally available platform. The interplay between theory and experiment continues to yield surprising discoveries and has already kept this field vibrant over many decades. Among the biggest mysteries in quantum Hall physics is the plateau at ν=5/2, widely expected to host highly prized non-Abelian anyons. Unlike many other fillings, where theory and experiment agree even quantitatively, its identity remains hotly debated. Our group's current research on the fractional quantum Hall effect focuses on the ν=5/2 state via questions that range from interpreting or proposing concrete experiments to more abstract theoretical questions.