llevar + time + gerundio: how long so far
Where English uses the present perfect continuous (I've been living here for two years), Spanish often uses llevar. The time span comes straight after llevar, the action follows in the gerundio. The neutral alternative is the present tense + desde hace.
The pattern
Same statement, different focus
Neutral
Vivo aquí desde hace dos años.
I've lived here for two years.
Te espero desde hace media hora.
I've been waiting for you for half an hour.
Duration in focus
Llevo dos años viviendo aquí.
I've been living here for two years now.
Llevo media hora esperándote.
I've been waiting for you for a good half hour.
For a stretch of time in which something has not happened, use llevar + time + sin + infinitive: Llevo meses sin verla (I haven't seen her for months).
Llevo meses sin verla.
I haven't seen her for months.
Llevaba dos noches sin dormir cuando por fin llamaron.
He hadn't slept for two nights when they finally called.
Change over time: venir, ir, andar, acabar
Four verbs of movement with the gerundio describe how an action unfolds over time. English would need words like for a while now, gradually, going around or in the end.
venir + gerundio: for a while now, up to today
An action repeats or develops from an earlier point up to now. Typical of news and reports.
Viene diciéndolo desde hace meses.
He's been saying so for months.
Los precios vienen subiendo desde enero.
Prices have been rising steadily since January.
ir + gerundio: little by little
A gradual development that is still going on.
Poco a poco voy entendiendo cómo funciona.
Little by little I'm getting the hang of how it works.
La situación va mejorando.
The situation is gradually improving.
andar + gerundio: going around doing
An action without a clear goal, repeated here and there. Colloquial and often disapproving.
Anda diciendo por ahí que lo van a ascender.
He's going around telling everyone he's getting promoted.
acabar + gerundio: end up doing
The outcome of a process, often after hesitation or against expectations.
Al final acabó aceptando la oferta.
In the end she accepted the offer after all.
Results and assumptions: tener and dar por + participle
Two periphrases with the participle focus on the state reached, not the process. With tener + participle, the participle agrees with the object: Tengo escritas tres páginas. With dar por + participle you declare something done or take it for granted.
Tengo entendido que la reunión se ha aplazado.
I understand the meeting has been postponed.
Llevo escritas tres páginas del informe.
I've got three pages of the report written so far.
llevar + participle shows progress so far
Doy por hecho que vendrás a la boda.
I'm taking it for granted that you'll come to the wedding.
Damos por terminada la reunión.
We'll call the meeting closed.