Alexander Ludwig

Vendsyssel Ludwig was signed by Vendsyssel FF in July 2012, which at that time still went under the name FC Hjørring.

After he had established himself as a starter for the club, Vendsyssel offered him a new contract in 2014, but Ludwig declined. As Ludwig's contract expired, clubs from the Superliga and Danish 1st Division were keen to sign him, but in the end he chose to sign with HB Køge, penning a three-year contract with the Danish second tier club.

HB Køge Ludwig made his debut for Køge in a 1–1 away draw against Skive IK on 25 July 2014. He scored his first goal for the club two months later, netting the 1–1 equalizer the 84th minute in a home match against Brønshøj, before Bruninho scored the winner for Køge four minutes later. Ludwig finished the season with 31 total appearances, in which he scored two goals.

Ludwig had a bad start to his 2015–16 season, suffering a knee injury in the season debut against Lyngby Boldklub on 30 July 2015 which kept him out for two months. He made his return to the starting eleven on 27 September, helping Køge advance in Danish Cup by scoring in a 2–0 win over AC Horsens. In the following league match Ludwig was in the starting eleven again and contributed to keeping another clean sheet as his club drew 0–0 away against FC Fredericia on 27 September.

On 29 November 2016, Ludwig was named Player of the Year for HB Køge after making 36 appearances and keeping 15 clean sheets throughout 2016.

Horsens On 8 June 2016, Ludwig signed a two-year contract with Danish Superliga club AC Horsens, after their head coach Bo Henriksen had referred to him as his "dream player". He made his debut on 14 July, playing the full match in a 2–1 away win over rivals AGF, marking his return to Danish top-tier football since his sole appearance for Midtjylland in 2011. Ludwig would have a strong season in the centre of defense alongside Bubacarr Sanneh, helping an overperforming Horsens-team reach the championship round where they eventually ended sixth in the league table. He capped off his season with 38 total appearances in which he scored three goals. He made his debut for the club on 15 July against newly promoted Vendsyssel FF, his former club, which ended in a disappointing 3–2 loss away at Nord Energi Arena. After a challenging first half of the season, where he was in and out of the starting lineup, Ludwig suffered a tear in the posterior cruciate ligament of his knee, which kept him out for some months. He made his return to the pitch in a 2–1 win over AGF in March, but would increasingly appear as a substitute for OB, especially into the next season.

Return to AC Horsens On 14 August 2019, AC Horsens announced that Ludwig had returned to the club on a four-year contract, as a replacement for the outgoing defender Sivert Heltne Nilsen. On 3 June 2020, Ludwig was voted into the "Team of the Week" of the Danish Superliga, after stringing together some strong performances in a rejuvenated Horsens-defense, beating league leader FC Midtjylland 1–0.

In summer 2026, AC Horsens announced that Ludwig will leave the club.