Alex was born in Belgrade on May 22nd 1984. When he was 8, his parents fled war-torn Yugoslavia to seek a better life in Britain. At school, Alex was persuaded by a tennis mad best friend, to take up the game. He says "At first it was just a social thing, a way of making friends in a new country." However, it soon became evident that he was blessed with a large amount of natural talent for the game.

  He started playing regularly on the international junior tour in 1999, competing against players like Mario Ancic, Marcos Baghdatis and Richard Gasquet who have gone on to reach the world's top 20.

  2001 was Alex's breakthrough year. From February to May he had an impressive run in which he won the Uruguay Bowl and then reached the semis of the Banana Bowl, a prestigious tournament in Brazil which attracts the world's best juniors. Both these tournaments were on South American clay, one of the toughest environments to play tennis in the world. Alex was rewarded by being named as one of the designated hitting partners for the Davis Cup tie against Portugal. Afterwards he said "The Davis Cup tie was unbelievable. It gave me all the motivation I need to keep working and maybe one day be a part of the full squad."  In August, Alex reached the final of the National junior Championships losing to the big-serving Norfolk right-hander, Richard Bloomfield. It had been an excellent year so far, but then two weeks in September and October were to catapult Alex into the British tennis spotlight. At just 17, he became the first British junior ever to reach the semis of the US Open, beating some of the world's best U18s along the way and then reached the final of the National championships, trouncing British no 3 and top 100 player Martin Lee 7-5, 6-0 in rd2 and beating Arvind Parmar [who has taken sets of Sampras and Rafter] in the semis before losing to Lee Childs. Just for good measure he then reached the Bolton challenger quarters the following week, scoring another week over Martin Lee. Alex was hailed as "the next Tim Henman," the new great hope for British tennis and the then Davis Cup captain Roger Taylor, famously compared his backhand to that of Rod Laver.

      When Great Britain were drawn to face Australia in rd1 of the world group in Sydney in January 2003, Alex would have expected to have been involved in the squad as a hitting partner at most. However, injuries to Greg Rusedski and Tim Henman meant that Alex was selected in the 4 man squad and nominated to play one of the live singles rubbers on the opening day. For most players, playing their first Davis Cup live rubber is a nerve-racking experience but playing it against the world no 1 and reigning Wimbledon champion Lleyton Hewitt in front of a full house of patriotic Aussie fans is not a task for the faint-hearted !  However, despite being ranked outside the top 500, it was Bogdanovic who made the better start, outplaying the world no 1 for much of the first set and at one stage he led 4-2. However, Hewitt fought his way back and managed to edge the 1st set 7-5. Hewitt won the next two sets 6-1, 6-2 but they were a lot closer than the scoreline suggests and many times Hewitt was forced to call on his renowed counter-punching ability, conjuring up several incredible passing shots from outside the tramlines. Alex was also selected to play the final rubber, with GB 4-0 down and seeking to avoid a whitewash. He faced on of the legends of the game Todd Woodbridge who has won all the Grand Slam doubles titles and dominated doubles for over a decade. However, he was simply outplayed by an inspired Bogdanovic who claimed his first Davis Cup victory with a 6-2, 7-6 win.             

2003 saw more breakthroughs for Alex, he reached his first challenger final in Surbiton [he is the only British player to date to reach the Surbiton final] beating several quality grass court players - George Bastl [who beat Sampras at Wimbledon 2002]  and Ivo Karlovic [who went on to shock Lleyton Hewitt in rd1 of Wimbledon three weeks later]. He won his first ATP match at Queens [a 3 set victory over Arvind Parmar] and he came within a whisker of beating Anthony Dupuis and reaching the 3rd round. Alex then shocked former Wimbledon quarter-finalist and top 10 player Jan Michael-Gambill in rd1 of ATP Nottingham before losing to 2000 Wimbledon semi-finalist Vladimir Voltchkov.

Alex endured a tricky first few months in 2004 but employing new coach Mike Raphael resulted in his form returning and he reached a futures final on clay in May and beat top 50 player Joachim Johansson in rd1 of ATP Nottingham. The Swede possesses one of the biggest serve-forehand combinations in the game but Alex successfully blunted the power and won in straight sets. A rd1 match against Roger Federer at Wimbledon on centre court followed. Federer won in straight sets but Alex was inspired by the experience and he had a superb run of results through July and August, reaching the final of the Nottingham and Manchester challengers [winning Manchester], making the semis of the Graz challenger in Austria on one of his least favourite surfaces and then qualifying for the US Open. Despite battling with the autumn New York humidity, Alex progressed through to the main draw without dropping a set, comprehensively thrashing Frenchman Julien Varlet 6-2, 6-2 in the final round. In rd1 he faced Alex Calatrava. The experienced Spaniard edged the first set but Bogdanovic hit back and took a 2 sets to 1 led before cramp started to set in. Calatrava raced through the 4th set 6-1 but Bogdanovic found a 2nd wind and came desperately close in the 5th set but Calatrava's extra experience eventually told and he won  it 6-4. This meant that Alex broke the world's top 200 for the first time.