Čepelová, who started playing tennis at the age of four, won the double junior title at the Australian Open in 2010 together with her compatriot Chantal Škamlová . In the same year she also won the bronze medal in singles and silver in doubles with Škamlová at the Summer Youth Olympic Games in Singapore . In 2010 she won the ITF tournament in Monastir . In 2011 further ITF titles followed in Stuttgart , Kristinehamn and Prague .
In the game against the Czech Republic in February 2011 in Bratislava, she first appeared for the Slovak Fed Cup team . She now has five wins and seven losses on her Fed Cup record.
Čepelová qualified for the first time in the main draw of a Grand Slam tournament in Wimbledon in 2012 . There she defeated Kristina Mladenovic and the former top 20 player Anabel Medina Garrigues before losing 3: 6 and 3: 6 against world number two Wiktoryja Asaranka . In 2013 she reached the peloton in all four Grand Slam tournaments and made it into the second round three times. After the US Open, she took a break due to an injury.
Since 2014
In the first round of the Australian Open in 2014, she failed to Bojana Jovanovski . In the second round of Charleston , she defeated world number one Serena Williams in straight sets . So she finished two series of Williams, 28 wins on clay in a row and 15 wins in Charleston in a row. Čepelová was after Katarína Studeníková , Daniela Hantuchová and Dominika Cibulková the fourth Slovak player to beat a current world number one. Just one day before her first round game at the Australian Open , Čepelová was hospitalized in January 2015; a two-month break followed and she lost her place in the top 100.