Zenga joined Inter Milan in 1982, after starting his professional career in 1978 in the lower divisions of Italian football (his first team was Salernitana in Serie C1, and he also played for Savona and Sambenedettese).

Initially, (in the 1982–83 season) he was the substitute of Ivano Bordon, who was one of the top Italian goalkeepers of his era, as he had been Dino Zoff's reserve in the 1982 FIFA World Cup.

However, Zenga played Inter's matches in the Coppa Italia, impressing enough that the club decided not to buy another goalkeeper after Bordon's decision to move to Sampdoria during the summer of 1983.

In Italy, Inter was the main rival of Hellas Verona who won the first and, to this day, only Scudetto of its history in 1985, while in Europe he had to suffer two bitter and quite controversial defeats at the hands of Spanish giants Real Madrid, both times in the UEFA Cup semi-finals.

[7] The 1989–90 and 1990–91 seasons proved to be bittersweet for Inter: although the team remained a title contender, it didn't manage to take another success on home soil, except for the victory in the Supercoppa Italiana played in November 1989 against Sampdoria.

However, Inter won the UEFA Cup that year, defeating, among the others, Aston Villa, Atalanta and Sporting CP on the road to the final against Roma.

[2] He had led the Revolution to their first playoff berth in team history,[14] and he finished the 1997 season with the second best goals-against average (1.27), second highest win total (15), and best league shootout record, allowing only 12 goals in 41 attempts.

[7] Zenga became the Italy national side's starting goalkeeper under manager Azeglio Vicini, ahead of his perceived career rival, Stefano Tacconi.

Here again Zenga was at the centre of controversy: in the first match against West Germany he conceded a free kick inside the penalty area due to having made too many steps while carrying the ball in his hands (an infringement rarely penalised).

Andreas Brehme, who would become Zenga's teammate at Inter only a few months later, scored from the resulting free kick to tie the game for West Germany.

[7][25][23] In the third-place match against England, Zenga conceded his second goal of the tournament when he was beaten by a David Platt header, although Italy managed to capture the bronze medal with a 2–1 victory.

[7][27][28] An aggressive, consistent, physically strong, complete, and athletic goalkeeper, Zenga was nicknamed Deltaplano ("Hang glider")[3][29][30][31] due to his excellent shot-stopping abilities, positioning, explosive reactions, bravery, and in particular for his speed, elegance, and agility, which enabled him to produce spectacular saves.

[3][7][25][31] Despite his reputation, the media was often critical of Zenga's penalty-saving record throughout his career,[25][31] although he stopped penalties against notable specialists, such as Roberto Baggio, Paul Merson and Michel Platini;[8] he was also criticised by pundits for his unsteady performances when coming out off his line to claim crosses, and performed best between the posts,[7][25][31][32] while he was also not particularly adept with the ball at his feet,[30] or very confident in his distribution,[33] and initially struggled in teams which employed a zonal marking defensive system and the offside trap, due to his reluctancy to rush out of goal.

[27] Nevertheless, he was able to adapt successfully to the changes in regulations following the introduction of the back-pass rule, and maintained a high level of performance as his career progressed, even as goalkeepers were required to play more frequently with their feet.

[34] In addition to his goalkeeping ability, Zenga also stood out for his strong mentality and leadership from the back, as well as his temper and flamboyant celebrations as a footballer,[8][27][35] and was also known for his composure under pressure, which enabled him not to be fazed if he ever made any errors.

[36] His other nickname, L'Uomo Ragno ("Spider-Man"),[3] is not related to his goalkeeping skills, but rather to a curious circumstance: in 1992, while answering questions about his exclusion from the Italy national team, Zenga softly sang a song by the Italian band 883, called Hanno ucciso l'Uomo Ragno ("Someone killed Spider-Man"),[28] which led pundits and supporters to call him like the Marvel Comics character.

In the summer 2006, Zenga was appointed as coach of Turkish Süper Lig side Gaziantepspor; however, after a poor start (five wins in 17 league matches), he resigned in January 2007 in order to accept an offer from United Arab Emirates club Al-Ain.

[42] Catania's playing style under Zenga was notable for the coach's focus on free kick planning; his assistant manager Gianni Vio is known to work exclusively on this particular side of football tactics during the weekly training sessions.

[43] He guided Catania to a mid-table finish and the Serie A points record for the eastern Sicilian side; at the final home game of the season he announced he was parting company with his club by mutual consent.

On 5 June 2009, after being linked with the managerial job at Lazio it was revealed that Zenga had agreed a three-year contract with Palermo to replace outgoing manager Davide Ballardini; the move was seen as a massive surprise due to the Rosanero club being rumoured to be interested in several other managers and the bitter rivalry between them and Catania, the only two Sicilian teams playing in the Italian top flight.

However, a number of disappointing results followed, ending in an unimpressive 1–1 home tie to Catania that led Palermo chairman Maurizio Zamparini to remove Zenga from his managerial duties on 23 November, after only thirteen league games in charge of the rosanero.

[51] On 30 July 2016, Zenga was appointed head coach of Football League Championship side Wolverhampton Wanderers for the 2016–17 season.

[53] On 2 August, he made his first signings, buying Icelandic striker Jón Daði Böðvarsson from Kaiserslautern and bringing in Portuguese midfielder João Teixeira on a season-long loan from Benfica.

[56] Zenga took Wolves on a six-game unbeaten run in all competitions, and eight points from his first four league games, including a 3–1 win at local rivals Birmingham City.

[58] Following the end of the summer transfer window, Zenga, having made ten new signings since his appointment, claimed that the Wolves squad was so strong that he could field two different teams if needed.

Zenga returned into management on 11 October 2018 as he was named new head coach of Serie B club Venezia in place of Stefano Vecchi.