Chelsea avoided a clash with Paris Saint-Germain during the draw in Nyon, Switzerland.
But they were instead paired up with La Liga champions Barcelona.
Manchester United were given a tie against Spanish side Sevilla.
And Tottenham have been matched with Serie A side Juventus.
Juve are struggling in their domestic league but have proven strong opposition so far in Europe.
Spurs will play in Turin in the first leg before the return fixture at Wembley.
Liverpool will play 2004 Champions League winners Porto – and will likely be happy with that draw considering who they could have faced.
Manchester City, likewise, take on one of the lesser-strength sides in Basel.
Another crunch clash in the last-16 is Real Madrid vs Paris Saint-Germain.
The two European giants will meet first at the Bernabeu after Real came second in their group behind Tottenham.
PSG signed Neymar in the summer specifically to help their Champions League efforts.
But they could be dumped out at the first knockout stage after this tough draw.
CHAMPIONS LEAGUE LAST-16 DRAW
BAYERN MUNICH vs BESIKTAS
CHELSEA vs BARCELONA
SHAKHTAR DONETSK vs ROMA
REAL MADRID vs PARIS ST-GERMAIN
SEVILLA vs MANCHESTER UNITED
PORTO vs LIVERPOOL
BASEL vs MANCHESTER CITY
JUVENTUS vs TOTTENHAM