Alén's passion for motorsport was inherited from his father, the 1963 Finnish champion in ice racing. He began rallying in 1969 driving a Renault 8 Gordini, finishing ninth on the 1000 Lakes Rally at his first attempt. After a stint with the Finnish Volvo importer, he secured a major works contract with Fiat following a combative performance on the 1973 RAC Rally, where he recovered from 178th place after a first-day roll to finish third overall. His physical conditioning programme with Fiat made him one of the first rally drivers to follow a formal fitness regime.
Alén joined the Fiat works team in 1974, initially driving the Fiat 124 Abarth Rallye. His first WRC victory came at the 1975 Rally Portugal, and he continued building his reputation through the mid-1970s as Fiat switched to the 131 Abarth. He won the 1976 1000 Lakes Rally and the 1977 Rally Portugal, contributing to Fiat's first manufacturers' championship in 1977. In 1978 Alén secured two wins and five consecutive podiums including a victory for Lancia's Stratos at the Rallye Sanremo, earning the FIA Cup for Drivers — the precursor to the World Championship for Drivers. He continued with Fiat through 1981, taking at least one win per season.
When Fiat wound down their works rally programme, Alén transferred to the closely affiliated Lancia team. He debuted the Lancia 037 in 1982, a rear-wheel drive car that proved particularly effective on asphalt. His victories with the 037 in 1983 helped Lancia edge Audi to that year's constructors' championship — the last rear-wheel drive car to win the title. Alén drove the 037 to its final WRC victory on the 1984 Tour de Corse before the four-wheel drive Lancia Delta S4 took over.
The 1986 season brought Alén's most painful near-miss. Following teammate Henri Toivonen's fatal accident in Corsica, Alén became unequivocal team leader and challenged Peugeot's Juha Kankkunen for the championship. He won the Rallye Sanremo after Kankkunen's Peugeot was excluded on a technicality; the title was provisionally his. Peugeot's subsequent appeal to the FISA, however, succeeded in having the results annulled, and the championship reverted to Kankkunen. Alén had held the title for exactly eleven days. As a public protest, he boycotted the 1987 Monte Carlo Rally.
Adapting successfully to Group A regulations introduced in 1987, Alén won three events in the Lancia Delta HF 4WD and added three more in 1988, culminating in a long-awaited first victory on the RAC Rally — an event he had pursued for fifteen years. That RAC win proved to be his final WRC victory.
In 1990 Alén joined the Prodrive-run Subaru World Rally Team, steering the Legacy to several top-five finishes as the programme established itself. A 1992 move to Toyota gave him a supporting role behind Carlos Sainz; in 1993 he took second for Toyota on the Safari Rally. He shared co-driving duties on the debut event of the Subaru Impreza at the 1993 1000 Lakes Rally alongside Ari Vatanen, but crashed on the opening stage. He also drove briefly in the International Touring Car Championship and DTM in 1995 for Alfa Romeo, and competed in the Trophy Andros ice-racing series in 1996–1997.
To mark his 50th birthday in 2001, Alén entered the Neste Rally Finland, finishing 16th overall in a Ford Focus WRC. He later competed twice in the Paris–Dakar Rally in the truck class, including a 2006 run for Iveco alongside Miki Biasion. In 2010 Ferrari president Luca di Montezemolo appointed Alén as a Ferrari test driver, beginning with snow tests in the Ferrari 458 Italia.
Alén's phrase "now maximum attack" became a widely cited piece of motorsport folklore. His 801 stage wins stood as the all-time WRC record for nearly three decades. The 1986 championship controversy remains one of the most debated injustices in rally history — the image of a driver holding a world title for eleven days before having it taken by administrative ruling defined his career far beyond the victories he did collect. His aggressive, never-surrender style influenced a generation of Finnish rally drivers who followed in his wake.