Fast radio bursts (FRBs) are mysterious millisecond pulses in radio, most of which originate from distant galaxies. Despite more than 50 theoretical models of FRB progenitors, their origin is still unknown. Therefore, revealing the origin of FRBs is becoming central in astronomy and astrophysics. After presenting some basic knowledge of FRBs, I will summarize the current observational constraints on the FRB progenitors, including our research results. FRBs are expected to be useful cosmic probes to investigate key science in astrophysics. I will talk about our recent results on testing general relativity using FRBs. At the end of the talk, I will introduce a new FRB telescope plan in Taiwan: Bustling Universe Radio Survey Telescope in Taiwan (BURSTT). The vast field of view and high duty cycle of BURSTT will provide us with the complete census of nearby FRBs with accurate localization. With such unique samples, BURSTT will overcome the bottlenecks that the current FRB facilities are facing. The unique capability of BURSTT will hold even after the future world-largest radio telescope, Square Kilometre Array (SKA), starts the science operation, allowing Taiwan to lead exciting science cases with FRBs.