1. To demand something by shrieking or shouting very loudly. The toddler screamed for more chocolate. The protestors gathered outside city hall, screaming for the mayor to repeal the controversial legislation.

2. By extension, to have or display an extremely high demand or desire for something; to clamor for something. The movie is so enthralling that it will leave you screaming for more. Fans have been screaming for news about the popular TV series for months.