Barcelona had been 1-0 down at home to Sevilla before David Villa and Leo Messi struck to seal another big win for the league leaders.
Real were 1-0 down at Deportivo and being completely outplayed, but bounced back thanks to strikes from Kaka and Gonzalo Higuain.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.