Micro-scale optical components play a crucial role in imaging and display technology, biosensing, beam shaping, optical switching, wavefront-analysis, and device miniaturization. Herein, we demonstrate liquid compound micro-lenses with dynamically tunable focal lengths. We employ bi-phase emulsion droplets fabricated from immiscible hydrocarbon and fluorocarbon liquids to form responsive micro-lenses that can be reconfigured to focus or scatter light, form real or virtual images, and display variable focal lengths. Experimental demonstrations of dynamic refractive control are complemented by theoretical analysis and wave-optical modelling. Additionally, we provide evidence of the micro-lenses' functionality for two potential applications-integral micro-scale imaging devices and light field display technology-thereby demonstrating both the fundamental characteristics and the promising opportunities for fluid-based dynamic refractive micro-scale compound lenses.