Davies was born in Neath, West Glamorgan. After spending time in the youth academy at Swansea City, he and his family moved to Viborg, Denmark, after his father accepted a job offer. They spent three years living in Denmark, where he played for Viborg FF's youth team before returning to Swansea. Davies attended Ysgol Gyfun Ystalyfera and is a Welsh speaker.
Club career
Swansea City
After spending time with the youth ranks, Davies signed a two-year contract with Swansea City, making his first-team debut against West Ham United for the Premier League on 25 August 2012, coming on as an 84th minute substitute for Neil Taylor in a 3–0 home win. Davies became a regular starter for Swansea in the 2012–13 season, following a long-term injury to Taylor. On 23 November 2012, Davies signed a new three-and-a-half-year contract with Swansea. On 19 January 2013, Davies scored his first goal for Swansea against Stoke City in a 3–1 victory. In doing so, at 19 years and 270 days, he became Swansea's youngest ever scorer in the Premier League. In September 2013, he scored his second and third Premier League goals for Swansea, against West Brom and Arsenal respectively. On 24 December 2013, Davies signed a one-year contract extension, keeping him at Swansea until June 2017.
Tottenham Hotspur
On 23 July 2014, Davies joined Tottenham Hotspur on a five-year contract for an undisclosed fee. He joined on the same day as his Swansea teammate Michel Vorm, with Gylfi Sigurðsson being exchanged as part of the deal. Davies made his Premier League debut for Tottenham Hotspur as a late substitute in a 0–3 defeat to Liverpool. He made his first start for the club in the league in a 2–1 away win at Hull City on 23 November 2014. He was an unused substitute for the 2015 League Cup Final at Wembley Stadium on 1 March 2015, in which Tottenham were beaten 2–0 by Chelsea. Davies scored his first goal for the club on 8 January 2017, a header in an FA Cup tie against Aston Villa. He signed a new four-year contract at Tottenham on 9 March 2017, extending his deal to 2021. Davies scored his second Tottenham goal—and his first for them in the Premier League—against Hull City on the final day of the 2016–17 season; a first-time strike from outside the box into the top left corner added a sixth goal in an eventual 7–1 win for Tottenham. Davies started for Tottenham in the opening match of the 2017–18 season, and scored a goal in a 2–0 win away to Newcastle United. Davies signed a new 5-year contract with Tottenham in July 2019.
International career
In September 2012, Davies was selected for the Wales squad for 2014 FIFA World Cup qualification matches in September 2012. He replaced club teammate Neil Taylor, who had suffered a broken ankle in a Premier League match against Sunderland. Davies made his full international debut in the 2–1 win against Scotland on 12 October 2012.