
der Vormarsch
advance
The forward movement of a military unit or army toward the enemy or in order to capture territory.
Der Vormarsch der Truppen wurde durch heftigen Widerstand gestoppt.
The advance of the troops was stopped by fierce resistance.
advance
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advance
The forward movement of a military unit or army toward the enemy or in order to capture territory.
Der Vormarsch der Truppen wurde durch heftigen Widerstand gestoppt.
The advance of the troops was stopped by fierce resistance.

rise / spread
The increasing spread, acceptance, or growing success of an idea, technology, or movement. Often used in the expression 'auf dem Vormarsch sein' (to be on the rise / to be gaining ground).
Flexible Arbeitsmodelle sind in vielen Branchen auf dem Vormarsch.
Flexible working models are on the rise in many industries.
The word is a clear compound of 'vor' (forward) and 'der Marsch' (the march). So it literally describes a march forward.
Der lange Marsch durch die Berge war sehr anstrengend.
The long march through the mountains was very exhausting.
In the figurative meaning, the fixed expression 'auf dem Vormarsch sein' (to be on the rise / to be gaining ground) is almost always used. It means that something is becoming increasingly popular, successful, or widespread.
Nachhaltige Produkte sind stark auf dem Vormarsch.
Sustainable products are strongly on the rise.
In a military context, 'Vormarsch' (advance) is often combined with verbs such as 'stoppen' (to stop), 'aufhalten' (to hold back), or 'fortsetzen' (to continue).
Die Armee konnte den feindlichen Vormarsch aufhalten.
The army was able to hold back the enemy advance.
You can recognize this figurative meaning when it is not about soldiers, but about abstract things. Typical subjects are ideas, technologies, trends, or social movements.
Die Digitalisierung ist in allen Lebensbereichen auf dem Vormarsch.
Digitalization is on the rise in all areas of life.
ascent / rise
The Aufstieg of a technology emphasizes its growing influence or economic importance. Vormarsch, by contrast, emphasizes that it is spreading further and becoming increasingly accepted. Aufstieg is appropriate for a stronger position, while Vormarsch is appropriate for its advance into more and more areas.

Der Vormarsch der Technologie in Büros und Privathaushalten ging sehr schnell.
The technology's spread into offices and private homes happened very quickly.
Der Aufstieg der Technologie zu einem wichtigen Wirtschaftsfaktor ging sehr schnell.
The technology's rise to become an important economic factor happened very quickly.