Drift follows a young Liberian refugee named Jacqueline (Cynthia Erivo) who has barely escaped her war-torn country to a Greek island. She offers massages to tourists in exchange for one or two euros to battle her hunger, while her daily struggle for survival keeps the memories that haunt her at bay. She meets an unmoored tour guide (Alia Shawkat) and the two become close as they each find hope in the other.