United staged a stunning comeback to beat PSG 3-1, going through on away goals following a 3-3 aggregate draw, while Harry Kane's goal at Signal Iduna Park saw Tottenham complete a 4-0 aggregate victory over Borussia Dortmund.
Could we see a Premier League showdown in the next knockout stage? Here's all you need to know...
The draw for the quarter-finals, semi-finals and final will be on Friday, March 15 in Nyon, Switzerland.
The scheduled start time is 11am and you will be able to follow the draw online with Sky Sports and on Sky Sports News.
There is no seeding or country protection at the quarter-final stages of the Champions League, meaning English sides could face each other. The team who is drawn first will play the first leg at home.
The quarter-final first legs take place on April 9-10 with the return legs on April 16-17.
The semi-final first legs are on April 30-May 1 before the second legs on May 7-8.
After the quarter-final and semi-final draws, there will be a draw for the final on the same day.
The draw for the final will determine the 'home' side for administrative reasons.
The final will take place at Atletico Madrid's Wanda Metropolitano Stadium on Saturday, June 1.
England's UEFA Nations League semi-final against Netherlands is on June 6, meaning a potential selection headache for manager Gareth Southgate should an English club - or two - reach the final.