[1][2][3] Hallman was part of a contingent of Swedish motorcyclists including; Bill Nilsson, Rolf Tibblin and Sten Lundin who dominated the sport of motocross in the early 1960s.

[1] He was recognized for his influential role in the development of American motocross in 2000 when, he was inducted into the AMA Motorcycle Hall of Fame.

[1][6] His father and older brother were both motorcycle racers, and they had built a practice motocross track on their farm where Hallman first learned to ride at the age of 13.

[6] Hallman possessed a smooth, efficient riding style, absorbing jumps with his legs so that his motorcycle flew at half the height of his competitors, which allowed the rear tire to begin applying power to the ground sooner.

He won his first European Championship heat race at the season-opening 250cc Spanish Grand Prix ahead of Dave Bickers and Jaromír Čížek.

[11] He won another heat race in East Germany ahead of Stig Rickardsson and Arthur Lampkin, but then broke his collarbone at 1960 250cc British Grand Prix which forced him to miss the remainder of the season.

[11] Hallman began the 1961 season with a string of top five results before winning his first overall victory at the 1961 250cc Finnish Grand Prix.

[14] After he had arranged a test ride with the Greeves factory, he was notified that the Husqvarna management had reluctantly agreed to repurpose some of the funding for their chainsaw division, and instead invest it into the development of a new 250cc motorcycle with a four-speed, two-stroke engine.

[18][19] Hallman successfully defended his crown in 1963, dominating the 1963 250cc World Championship by winning eight of the fourteen rounds to take the title over three ČZ factory team riders.

[24] Robert took full advantage of the ČZ factory support to win 9 of the 14 Grand Prix races to claim the world championship ahead of second-placed Hallman.

[28] In 1965, Hallman was completing his senior year in college and the heavy workload meant he had to reduce his racing schedule, yet he still managed a fourth place in the 1965 250cc World Championship.

[8][29] Russian ČZ rider Victor Arbekov won five Grand Prix races to claim the world championship ahead of the defending champion Joël Robert.

[31] Husqvarna produced a new race bike for 1966 with a new, rigid frame that placed the engine lower so that handling was improved.

[35] During his free time, Hallman also participated in Swedish auto rally racing competitions, driving a Saab 96 with his older brother, Hans, serving as his co-driver.

[29] After Robert won three consecutive Grand Prix races in France, Holland and West Germany to take the early points lead, Hallman then won three races in Russia, Yugoslavia and Sweden to tie Robert for the championship points lead as they went into the final round in Austria.

[43][44] Hallman was a member of a victorious Swedish team at the 1968 Trophée des Nations event for the fifth and final time in his career.

Hallman was instrumental in Yamaha's decision to purchase the patent for an innovative single shock absorber rear suspension designed by Lucien Tilkens, a professor at the Liege Engineering College in Belgium.

[52][53] Having seen the benefits of the suspension for himself, Hallman convinced Yamaha team manager, Mr. Kuratomo, that the new invention was worth developing.

[52] The suspension design which became known by the trade name Monoshock, helped Håkan Andersson win the 1973 250cc motocross world championship for Yamaha and would go on to revolutionize the sport.

[54] Åberg rode the bike to a victory in the first moto of the 1977 500cc Luxembourg Grand Prix and ended the season ranked 9th in the final world championship standings.