verbs
challenge the honesty or veracity of
"the lawyers tried to impeach the credibility of the witnesses"
is a type of (narrower)
issue a challenge to
"Fischer challenged Spassky to a match"
charge (a public official) with an offense or misdemeanor committed while in office
"The President was impeached"
is a type of (narrower)
file a formal charge against
"The suspect was charged with murdering his wife"
bring an accusation against; level a charge against
"The neighbors accused the man of spousal abuse"