Spurs welcome the Dutch outfit to North London for the first leg on Tuesday night having toppled Manchester City in the quarter-finals, but they will be wary of an Ajax side that has already eliminated Real Madrid and Juventus.
Not since their first ever European campaign in 1961-62 have Spurs made it to the semi-finals of this competition, but they will now believe that they have what it takes to go all the way.
Eusebio's Benfica ended their journey on that occasion, but the current crop are perhaps Tottenham's best team since the glory days under Bill Nicholson and all that is missing is a trophy to mark their continued progress under Mauricio Pochettino.
There would be a certain degree of irony if Tottenham's 11-year trophy drought was to be ended by the most coveted prize of them all, although as the only one of the four remaining teams not to have reached the final before they are already at a disadvantage in the experience stakes.
To have even made it this far is an achievement for which deserves huge credit considering Pochettino has had to deal with a relatively shallow squad, having not made a single signing in either transfer window this season.
Spurs are also still in control of their own fate when it comes to qualifying for the competition again next season, despite slumping to an underwhelming 1-0 defeat at home to London rivals West Ham United on Saturday.
It is now three losses in their last four games across all competitions, and Saturday's result also ended their perfect start to life at their new stadium - far from ideal preparation for one of the biggest matches in the club's history.
Pochettino's side were also in relatively poor form before they welcomed Man City to North London in the quarter-finals, though, and they will no doubt draw belief from their thrilling aggregate victory over the English champions.
Spurs have scored just one goal in three games since the ball bounced off Fernando Llorente's hip in the second-leg classic of that tie, and the stretched nature of their squad was highlighted against the Hammers when they ended the match with Llorente and Vincent Janssen up front.
Pochettino has hinted that Harry Kane might be fit to feature in the Champions League final should Spurs make it that far, but for now they must find a way to cope without their talisman - and the suspended Son Heung-min - if they are to end Ajax's run.
Recent Champions League form: WDWWWL
Recent form (all competitions): WWLLWL
Ajax's wait to grace this stage of the Champions League has not been quite as long as Tottenham's, but it has still been 22 years since they made it this far and football purists will be delighted to see such a great club upset the odds.
The ever-increasing importance of money in football has lessened the Dutch outfit's capacity for continental dominance, but every so often a particularly special young group of players break through from their famous academy to drag them back amongst Europe's elite.
That was the case the last time they won this trophy in 1995, when the likes of Patrick Kluivert, Marc Overmars, Clarence Seedorf, Edgar Davids and Ronald and Frank de Boer truly launched their hugely successful careers.
The current crop led by Matthijs de Ligt and Barcelona-bound Frenkie de Jong look more than capable of emulating that golden era, and the knowledge that neither is likely to still be there next season will make the latter stages of this campaign all the more important to savour.
Ajax's business model means that a sustained spell at Europe's top table is unlikely, but they have already ended Real Madrid's reign in this season's competition before doing the same to Cristiano Ronaldo with victory over Juventus in the quarter-finals.
The manner of those triumphs should leave Ajax full of confidence that they can not only get past Spurs, but also provide another upset in the final with either Barcelona or Liverpool sure to go into the Madrid showpiece as favourites.
Erik ten Hag's side have enjoyed their best moments of this season's competition away from home too, with those memorable victories at the Bernabeu and in Turin as well as a draw against Bayern Munich in the group stages.
However, they have only won two of their previous eight away legs in the Champions League semi-finals, including a defeat at this stage to Nottingham Forest in 1980 as Brian Clough's side went on to retain the trophy.
Indeed, Ajax have lost their last four two-legged ties against English clubs, and there is also the factor of a thrilling title race in the Eredivisie to consider with only goal difference separating them from PSV Eindhoven going into the final two games of the season.
Ajax will also face Willem II in the KNVB Beker final this weekend, so a treble remains on the cards in what has been a memorable season already, and the Champions League leg of that is surely the one they will covet the most.
Recent Champions League form: WDLWDW
Recent form (all competitions): WDWWWW
Kane is now out of his protective boot and walking normally, but he remains sidelined and only has a chance of featuring again this season if Spurs reach the final.
Son has often been the man to step up in Kane's absences this season, but he too is unavailable for this match due to an accumulation of yellow cards in the competition so far.
Ajax's involvement in the semi-finals prompted the Eredivisie to postpone a full round of fixtures in order to give them more time to recover.
Noussair Mazraoui suffered an ankle injury in the second leg against Juventus but is now back in training and could be available for selection.
Former Southampton man Dusan Tadic is expected to lead the line once again, having scored 31 goals and created 15 more across all competitions this season.
Tottenham possible starting lineup:
Lloris; Trippier, Alderweireld, Vertonghen, Davies; Eriksen, Dier, Alli, Rose; Llorente, Lucas
Ajax possible starting lineup:
Onana; Veltman, De Ligt, Blind, Mazraoui; Schone, De Jong; Ziyech, Van Beek, Neres; Tadic
Head To Head
These two sides have only faced off in one previous European tie, with Spurs running out 6-1 aggregate winners in the first round of the 1981-82 Cup Winners' Cup.
Spurs won the home leg of that tie 3-0, although that is Ajax's only previous defeat in London having otherwise won once and drawn twice in the English capital.
Tottenham have only ever lost one home game against Dutch opposition and are six matches without defeat to an Eredivisie outfit stretching back to 2007.
We say: Tottenham 1-1 Ajax
Spurs do not draw many games, but some of their feeling of invincibility at their new home will have deserted them after the weekend defeat and Ajax are a team in fine form. The visitors have scored a Dutch-record 160 goals across all competitions this season and will fancy their chances of getting at least one more away from home on Tuesday.