The mechanisms that trigger strong bursts of star formation in dwarf galaxies are poorly understood. Blue Compact Dwarfs (BCDs) are nearby starburst galaxies that may hold the key to understand these mechanisms. We are studying a sample of 18 BCDs using both new and archival HI data. In several cases, we find that BCDs have a steeply-rising rotation curve that flattens in the outer parts. This points to a strong central concentration of mass. We introduce a new parameter to quantify the central mass concentration in galaxies: the circular-velocity gradient V(Rd)/Rd, where Rd is the galaxy scale-length. We find that V(Rd)/Rd correlates with i) the central surface brightness; ii) the mean HI surface density over the stellar disk; and iii) the SFR density. BCDs have higher V(Rd)/Rd than typical dwarf irregulars, suggesting that the starburst activity is closely linked with the gravitational potential and the concentration of gas. We decompose the rotation curves of BCDs into mass components and find that baryons (stars and gas) are dynamically important. This is remarkable, as dwarf galaxies are commonly thought to be entirely dominated by dark matter. We discuss the implications of these results on the evolution of dwarf galaxies and in particular on the properties of the progenitors and descendants of BCDs. Finally, we discuss interactions/mergers or cold gas accretion as likely explanations for the triggering of the starburst.