Alén's passion for motorsport came directly from his father, the 1963 Finnish ice-racing champion. He began rallying in 1969 behind the wheel of a Renault 8 Gordini and immediately showed promise, finishing ninth on the 1000 Lakes Rally at his first attempt. Subsequent drives for the Finnish Volvo importer brought third-place finishes at the 1000 Lakes in both 1971 and 1972, and at his World Rally Championship debut — the 1973 1000 Lakes — he took second behind Timo Mäkinen.
Strong performances at his home event attracted interest from Fiat and Ford. A notable drive in the 1973 RAC Rally with a Ford Escort RS 1600 — recovering from a roll that dropped him to 178th place to finish third — earned Alén a contract with Fiat. He also became the first rally driver assigned a personal fitness programme.
Racing the Fiat 124 Abarth Rallye in 1974 and 1975, he secured his first WRC win at the 1975 Rally Portugal. The 1976 introduction of the Fiat 131 Abarth brought further victories: the 1976 1000 Lakes and the 1977 Rally Portugal, contributing to Fiat's first manufacturers' title that year. In 1978, Alén won twice with the 131 Abarth and once in a Lancia Stratos at the Rallye Sanremo, clinching the FIA Cup for Drivers — the precursor to the formal World Championship for Drivers — well ahead of Jean-Pierre Nicolas and Hannu Mikkola. Fiat took their second manufacturers' crown the same season. Alén continued with Fiat through 1981, taking at least one win per season.
After Fiat closed its works rally programme, Alén transferred to the related Lancia outfit. In 1982 he debuted the Lancia 037, the marque's first Group B homologated car, a rear-wheel-drive machine particularly suited to tarmac. His wins in 1983 helped Lancia narrowly edge Audi for the constructors' title. The 037's final victory came at Alén's hands on the 1984 Tour de Corse, before he transitioned to the four-wheel-drive Lancia Delta S4 for the closing rounds of 1985.
Following the death of teammate Henri Toivonen in Corsica in 1986, Alén became the undisputed Lancia team leader and pushed hard for the drivers' title. After Peugeot's entries were excluded from the Rallye Sanremo on a controversial technicality, Alén notched a victory that briefly placed him atop the standings. Peugeot appealed the decision, the FIA's sporting body eventually annulled the Sanremo results, and Alén was stripped of a World Championship he had held for just eleven days. His rival Juha Kankkunen was declared champion. Alén responded by boycotting the 1987 Monte Carlo Rally in protest.
He adapted well to the replacement Group A regulations with the Lancia Delta HF 4WD, winning three events in 1987, though a televised rollover on the RAC Rally cost him a probable second place in the overall standings. Three more wins followed in 1988, the last of which was an emotionally charged debut victory on the RAC Rally — an event he had been chasing for fifteen years. It proved to be his final WRC win.
In 1990, Alén joined the Prodrive-run Subaru World Rally Team, contributing to several early results with the Subaru Legacy. For 1992 he moved to Toyota, largely in a supporting role behind Carlos Sainz. The 1993 season saw him share drives between Toyota and Subaru, taking second for Toyota on the Safari Rally and co-driving the Subaru Impreza on its debut at the 1000 Lakes, where a first-stage crash ended his run. This effectively concluded his time as a frontline rally driver.
Alén also competed in two rounds of the 1995 International Touring Car Championship for Alfa Romeo and raced in DTM earlier that year. He entered the Trophy Andros ice racing series in 1996 and 1997, and to mark his 50th birthday he returned to the 2001 Neste Rally Finland in a Ford Focus WRC, finishing sixteenth overall. He participated in the Paris-Dakar rally twice in the truck class, including a 2006 entry for Iveco alongside Miki Biasion.
Alén's career total of 19 WRC victories places him among the most successful rally drivers of his era, yet he never claimed the drivers' world title — a result of the sport's points system, competitive timing, and the infamous 1986 Sanremo annulment. His 801 stage wins stood as the all-time record for nearly three decades. The phrase "now maximum attack" entered popular rally culture as shorthand for commitment on a stage, and his name remains synonymous with an era of flat-out, hard-charging Finnish driving style.