The phrase "kept up with" refers to maintaining pace with something or someone. Synonyms for this phrase include "managed to keep abreast of," "stayed on top of," and "followed closely." Other alternatives may include "kept pace with," "maintained progress with," and "remained current with." Often, people use this phrase in discussing current events, new trends, or social media, so some additional synonyms can be "stayed in the loop," "remained informed of," and "followed the latest developments." All of these synonyms convey the same idea - to stay updated, to stay current, and to keep pace with the changes happening around us.