This paper presents a comprehensive study of cavitation bubble dynamics inside a droplet suspended in another host fluid, both theoretically, experimentally, and numerically. The theoretical framework introduces a modified Rayleigh collapse time and natural frequency for spherical bubbles, influenced by the density ratio between the two liquids and the bubble-to-droplet size ratio. Experimental investigations were conducted for laser-induced cavitation bubbles in oil-in-water (O/W) and water-in-oil (W/O) droplets, revealing distinct fluid-mixing mechanisms. In O/W droplets, a liquid jet forms around the end of the bubble collapse phase, penetrating the droplet interface. In W/O droplets, the bubble traverses the droplet interior, leading to global motion and eventual droplet pinch-off when the local Weber number exceeds a critical value. The boundary integral model accurately captures the dynamics of nonspherical bubbles, and a parametric study is performed to investigate bubble-droplet interactions. The findings have significant implications for applications such as ultrasonic emulsification and pharmacy.This paper presents a comprehensive study of cavitation bubble dynamics inside a droplet suspended in another host fluid, both theoretically, experimentally, and numerically. The theoretical framework introduces a modified Rayleigh collapse time and natural frequency for spherical bubbles, influenced by the density ratio between the two liquids and the bubble-to-droplet size ratio. Experimental investigations were conducted for laser-induced cavitation bubbles in oil-in-water (O/W) and water-in-oil (W/O) droplets, revealing distinct fluid-mixing mechanisms. In O/W droplets, a liquid jet forms around the end of the bubble collapse phase, penetrating the droplet interface. In W/O droplets, the bubble traverses the droplet interior, leading to global motion and eventual droplet pinch-off when the local Weber number exceeds a critical value. The boundary integral model accurately captures the dynamics of nonspherical bubbles, and a parametric study is performed to investigate bubble-droplet interactions. The findings have significant implications for applications such as ultrasonic emulsification and pharmacy.