With Gladbach Veh played in the 1980 UEFA Cup final, losing against Eintracht Frankfurt.

Due to injuries he played only eight games in the second Bundesliga for SpVgg Bayreuth before retiring in November 1990.

[1] Veh was head coach of Greuther Fürth between 1 July 1996 and 14 October 1997.

[4] Veh also led the team to a Round of 16 berth in the German Cup where they lost 3–1 to Karlsruher SC.

[7] Reutlingen's final win of the 1998–99 season came on matchday 28 against Bayern Munich II[7] when they were two points outside the Promotional playoff for the 2.

[11] In the 2000–01 season, Reutlingen finished in seventh place and 10 points outside the promotion zone.

[16] In the 2002–03 season, Veh led Hansa Rostock to a 13th-place finish in the Bundesliga[17] and Round of 16 in the German Cup.

[24] Veh was hired by VfB Stuttgart to replace Giovanni Trapattoni on 10 February 2006.

In May 2007, Veh and VfB Stuttgart scored their biggest successes by winning the Bundesliga on 19 May 2007 and qualifying for the DFB Cup final, which gave Veh and his team the chance to win the "double".

On 23 November 2008, Veh parted ways with VfB Stuttgart, due to the club's current performances.

[29] His dismissal came in the wake of a 4–1 defeat away at VfL Wolfsburg and a 5 match winless streak.

[30] On 23 May 2009, it was announced that Veh would take over newly crowned Bundesliga champions VfL Wolfsburg from the hands of Felix Magath in July.

[35] On 13 March 2011, Veh was sacked by HSV, following a 6–0 hammering by Bayern Munich in the Bundesliga, six points adrift from a spot that would have allowed them to play in the UEFA Europa League the following season.

[38] After achieving promotion to the Bundesliga in his first season, Veh renewed his expiring contract with Frankfurt for another year.