klagen über
to complain about
To complain about something negative or express one's suffering about it.
Die Mitarbeiter klagen über die hohe Arbeitsbelastung.
The employees complain about the heavy workload.

to complain / sue / lament
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to complain about
To complain about something negative or express one's suffering about it.
Die Mitarbeiter klagen über die hohe Arbeitsbelastung.
The employees complain about the heavy workload.

You can recognize the meaning of 'klagen' from the preposition: 'klagen über' means to complain, 'klagen gegen' means to sue someone. Without a preposition in an emotional context, it often means 'to wail' or 'to express grief'.
Er klagt über das schlechte Wetter.
He complains about the bad weather.
The verb 'klagen' is closely connected to the noun 'die Klage'. 'Die Klage' can mean both a complaint and a lawsuit in court.
Der Anwalt hat die Klage beim Gericht eingereicht.
The lawyer filed the lawsuit with the court.
When you complain about something, always use the preposition 'über' followed by the accusative. This pattern is fixed.
Viele Menschen klagen über zu viel Stress bei der Arbeit.
Many people complain about too much stress at work.
In the legal sense, 'klagen' is used with 'gegen' + accusative (the person/company) or 'auf' + accusative (the goal, e.g., damages).
Das Unternehmen klagt auf Schadensersatz in Höhe von einer Million Euro.
The company is suing for damages amounting to one million euros.
to cry
'weinen' and 'klagen' can both have to do with pain, grief, or dissatisfaction. 'weinen' mainly describes tears: a person is sad, in pain, or very moved. 'klagen' more often means that someone expresses their suffering or complains about something negative. You do not have to cry when doing this. The words can be confused because 'weinen' can also colloquially mean something like 'to whine'. In normal usage, the rule is: when there are tears, say 'weinen'; for complaints or loudly expressed suffering, you are more likely to say 'klagen'.

Wegen der vielen Überstunden klagen mehrere Kollegen über starke Müdigkeit.
Because of all the overtime, several colleagues complain about being extremely tired.
Meine Freundin weint nach dem Gespräch, weil sie sehr enttäuscht ist.
My friend cries after the conversation because she is very disappointed.