Beck has won two singles and one doubles title on the WTA tour, as well as seven singles titles on the ITF circuit in her career. On 18 July 2016, she reached her best singles ranking of world number 37 and on the same date, she peaked at world number 84 in the doubles rankings.
Beck's father, Johannes, and mother, Petra, teach chemistry at the University of Bonn. Beck attended the Erzbischöfliche Liebfrauenschule Bonn, a school for girls, where she completed her Abitur in 2011.
Beck started 2012 ranked world number 234. She played one ITF tournament in January, one in February, and three in March. She was runner-up in Sunderland and Bath and won in Moscow. In April and May, Beck played higher-level tournaments, but had to play qualifying rounds. She qualified for the main draw in Copenhagen and Prague, achieving the second round of the main draw at the latter. She lost in qualifying at the events in Stuttgart and Estoril, and at the French Open. She did, however, take part in the Junior French Open, defeating Anna Karolína Schmiedlová in the final in three sets.
Beck played in the qualifying rounds of Wimbledon, earning a place in the main draw, but lost in the first round. In July, she played the qualifying rounds at the WTA tournament in Båstad, earning a spot in the main draw. Again, she lost in the first round. She also played two ITF tournaments, winning the $50,000 ITF event in Versmold, and losing in the second round at the $100,000 ITF event in Olomouc. In August, she won a $25,000 ITF tournament in Koksijde, then played in qualifying for the US Open, losing in the first round. In September, she played at the 2012 Bell Challenge in Quebec City, with her rank now high enough to earn direct entry into the main draw. In Canada, she won in the first round, but lost in the second. She then went on to win the 2012 Aegon GB Pro-Series Shrewsbury on the ITF tour. In October, she played two WTA events, but had to play qualifying rounds. She lost in the second round of qualifying at the 2012 Generali Ladies Linz, but won through to the main draw at the 2012 BGL Luxembourg Open, winning her first-round match but losing to Lucie Hradecká in the second. Back on the ITF circuit, she won the two $75,000 events in Ismaning and Barnstaple. She ended 2012 with a ranking of world number 78.
In 2013, Beck reached the quarterfinals of the 2013 Shenzhen Open, defeating the number four seed Hsieh Su-wei in the second round. She then went on to win her first Grand Slam match at the 2013 Australian Open, shocking the number 28 seed Yaroslava Shvedova in round one before going out to Ayumi Morita of Japan. Beck then played WTA main tour events, with her ranking now giving direct entry into the main draw. She lost first round in Pattaya City and Memphis, but advanced to the second round in Florianópolis. Beck then played at the Premier tournaments in Indian Wells and Miami, losing in the first round of each. In April, Beck achieved her best WTA International result in Katowice, achieving her first career International-level semifinal, losing to world number 13 Roberta Vinci. Beck then played the WTA Premier tournament in Stuttgart, losing in the first round to world number 8 Petra Kvitová.
At the 2013 French Open, Beck reached the second round before losing to Victoria Azarenka in straight sets. She also reached round two at Wimbledon, losing to Klára Zakopalová in straight sets. However, at the US Open, she lost to Elena Vesnina in the first round.
Beck improved her previous year's result at the Shenzhen Open, this time reaching the semifinals, where she lost to Li Na in straight sets. At the 2014 Australian Open she defeated Croatian Petra Martić in the first round, but lost to 14th seed Ana Ivanovic in the second. At the French Open, she lost in the first round to Bulgaria's Tsvetana Pironkova in the first round in three sets.
In October, Beck won her first WTA title by emphatically defeating Barbora Záhlavová-Strýcová in the Luxembourg Open final.
At the 2015 French Open, Beck defeated former world number two Agnieszka Radwańska in the first round in three sets, becoming just the third player to defeat the Pole in the first round of a Grand Slam tournament. In round two, she defeated another Pole in the form of qualifier Paula Kania to reach the third round of a Grand Slam tournament for the first time. After early exits at Wimbledon and the US Open and her first WTA doubles title, Beck won her second WTA singles title at the Coupe Banque Nationale by beating Jelena Ostapenko (who had defeated her in their last meeting) in straight sets.
After early exits at the Shenzhen Open and the Hobart International, Beck reached the second week of a Grand Slam for the first time at the 2016 Australian Open,beating wildcard Priscilla Hon, No.11 seed Timea Bacsinszky and Laura Siegemund en route. She then lost to eventual champion Angelique Kerber in straight sets. After that, Beck played for Germany in their Fed Cup tie against Switzerland and where she beat Bacsinszky once again. However, the win was not enough for them as Germany lost in the doubles match.