A historic week beckons for the two British clubs as they prepare for their first leg Europa League semi-final games against RB Leipzig and Eintracht Frankfurt.
While a European trophy is undoubtedly a major motivation, automatic entry in to the Champions League is also a goal pursued by all four of these clubs.
No team in world football has won as many league titles as Rangers. However, despite their domestic heroics, the club have only ever won one European trophy in their 150-year history - the 1972 European Cup Winners' Cup.
West Ham haven't pulled up many trees on the continent either, winning the 1965 European Cup Winners' Cup as well as the 1999 UEFA Intertoto Cup.
RB Leipzig were formed just 12 years ago, however they're already Champions League semi-finalists having made the last four back in 2020.
Eintracht, on the other hand, have the most glowing European CV considering they made a European Cup final and won the 1960 UEFA Cup as well as the 1967 UEFA Intertoto Cup.
Here, we take a closer look at both semi-finals.
RB Leipzig vs Rangers
Despite going through a managerial change earlier in the campaign, this could turn out to be a strong season for RB Leipzig. The team are on course for a top-four finish in the Bundesliga and could yet end the season with a DFB Pokal/Europa League cup double.
Rangers have fallen six points behind in the Premiership title race but are eyeing two cup wins under Giovanni van Bronckhorst, after the Gers beat Celtic at Hampden to make the Scottish Cup final.
Those are probably the only similarities between two clubs which couldn't be any more different. While Rangers are a club based on history and tradition, RB Leipzig are the epitome of the modern football landscape.
RB Leipzig's 15-match unbeaten run came to an end this past weekend as they fell to a 2-1 home defeat against Union Berlin. The visitors scored two goals in the final four minutes to hand Domenico Tedesco just his third defeat as Leipzig boss.
Interestingly, that was the first time in over two months (13 games) that RB had conceded more than one goal in a game.
Rangers haven't been as cerebral having lost three of their last eight games. However, Van Bronckhorst's side are in the midst of a four-match winning run and are capable of causing problems away in Germany.
In their last game, the defending Scottish champions beat Motherwell 3-1 to maintain their six-point gap to Celtic.
Europa League knockout-stage journey
RB Leipzig 5-3 Real Sociedad
Borussia Dortmund 4-6 Rangers
RB Leipzig (walkover) Spartak Moscow
Rangers 4-2 Crvena Zvezda
RB Leipzig 3-1 Atalanta
Braga 2-3 Rangers
West Ham vs Eintracht Frankfurt
Unlike Rangers and RB Leipzig, these two clubs have a lot more in common. Both, for instance, have faced relegation in recent years. Both have also come back strong and are now challenging the status quo in their respective leagues.
The trouble is, both West Ham and Eintracht Frankfurt have endured some tough results over the last few weeks, meaning their hopes of European qualification for the following campaign rest on this ongoing Europa League campaign.
Financial benefits of winning this competition are significant, but playing Champions League football next year could be the spark which pushes one of these two clubs onto the next level.
West Ham have done well to keep up with their top-six challengers for the majority of the Premier League season, but it appears the Hammers are beginning to run out of steam in the crucial time of the campaign.
One win from their last five games has seen David Moyes' men drop to seventh in the standings - still just two points away from Manchester United.
In their last outing, the Hammers were narrowly beaten by Chelsea at Stamford Bridge as Christian Pulisic bagged the only goal of the game in stoppage time.
Eintracht have suffered a similar fate. Their hopes of fighting for the top six in the Bundesliga were dashed by a poor run of form in recent weeks.
In fact, Eintracht have won just one of their last eight games. Interestingly, that one victory came away at Camp Nou as they beat Barcelona 3-2 to set up their semi-final date with West Ham.
Europa League knockout-stage journey
West Ham - bye
Eintracht Frankfurt - bye
Sevilla 1-2 West Ham
Real Betis 2-3 Eintracht Frankfurt
West Ham 4-1 Lyon
Eintracht Frankfurt 4-3 Barcelona