Spain outlasted the Netherlands over 120 minutes to seal their spot in the final four, while Sweden edged out Japan in their quarter-final tie.
Match preview
Spain already made history at the tournament when they thrashed Switzerland 5-1 in the last-16 to reach the Women's World Cup quarter-finals for the very first time.
La Roja continued to forge more memorable moments in their quarter-final tie against the Netherlands, which saw Jorge Vilda's side prevail following 120 minutes of captivating action.
The momentum appeared to swing in favour of the Dutch when Stefanie Van der Gragt scored a stoppage-time equaliser to cancel out Mariona Caldentey's first-half penalty, but Spain wrestled back control to find a winner in extra-time courtesy of Barcelona youngster Salma Paralluelo.
Spain are now preparing to appear in a major tournament semi-final for the first time since reaching the final four of the 1997 European Championships.
No team has scored more goals at the tournament than La Roja, who have scored 15 goals along their Women's World Cup journey, and they will be determined to showcase that firepower on Tuesday.
After ousting the defending champions USA in a dramatic penalty shootout, Sweden turned their attention to another tough test against Japan in the quarter-finals.
Japan entered the contest in impressive form after winning their opening four games of the tournament by a combined 14-1 scoreline, but Sweden showed no signs of fear and quickly asserted their authority in a dominant first-half performance, where they took the lead thanks to Amanda Ilestedt's 32nd-minute strike.
Sweden doubled their advantage within six minutes of the restart courtesy of a Filippa Angeldahl penalty, before Japan spurned their chance to score from the spot when Riko Ueki thumped her effort against the crossbar.
Although Japan eventually pulled a goal back through Honoka Hayashi, the Europeans held firm to book their place in the World Cup semi-finals for the fifth time in their history.
Sweden have tended to struggle at this stage of the competition, losing three of their previous four semi-final appearances, but they will be hoping for a repeat of their only last-four victory, which took place against Canada in the 2003 tournament.
Spain Women Women's World Cup form:
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Sweden Women Women's World Cup form:
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Team News
After being forced off in the second half against the Netherlands, Spain's Laia Codina is a doubt for Tuesday's semi-final tie.
Aitana Bonmati picked up a knock in Friday's victory, but the Barcelona midfielder is expected to be fit to take her place in the lineup.
Paralluelo, who dropped out of the side for the quarter-final, is set to return to the Spain frontline after scoring the winning goal against the Dutch.
As for Sweden, Peter Gerhardsson may be tempted to select the same starting lineup for the third consecutive game.
Ilestedt will resume her formidable central defensive partnership with Magdalena Eriksson, while Nathalie Bjorn and Jonna Andersson will operate as the two-full backs.
Arsenal striker Stina Blackstenius will continue to lead the line, while the width will be provided by Johanna Rytting Kaneryd and Fridolino Rolfo.
Spain Women possible starting lineup:
Coll; Hernandez, Paredes, Codina, Batlle; Bonmati, Abelleira, Hermoso; Paralluelo, Caldentey, Gonzalez
Sweden Women possible starting lineup:
Musovic; Bjorn, Ilestedt, Eriksson, Andersson; Angeldahl, Rubensson; Rytting Kaneryd, Asllani, Rolfo; Blackstenius