Dark matter is a hypothetical matter in the universe introduced to coherently explain observations ranging from the scale of galaxies to the whole of the universe. The DarkSide program is a direct dark matter detection experiment that utilizes dual-phase argon time projection chambers. Its preceding experiment, DarkSide-50, has set the most stringent exclusion limits for several light dark matter candidates. Owing to its peculiar behavior, dark matter can be searched for in a model-independent way exploiting the expected fluctuation of the relative velocity between dark matter and the Earth. I will present the result of the search for an event rate modulation caused by such a fluctuation using argon for the first time, following an overview of the recent light dark matter searches. Furthermore, I will describe efforts towards a newly proposed detector, DarkSide-LowMass, optimized for the detection of light dark matter.