ADJ

big, considerable, enormous, great, huge, radical, real, serious, significant, strong
difficult, tough
major, main
fresh, new
exciting, interesting
economic, environmental, intellectual, political, technical, technological
Liszt's piano music presents an enormous technical challenge

VERB + CHALLENGE

be, pose, present
face, meet, respond to, rise to, take on/ up
The gallery has risen to the challenge of exhibiting the works of young artists. He has taken on some exciting new challenges with this job

CHALLENGE + VERB

face sb
the challenges facing nurses in casualty

ADJ

serious
direct
effective
legal

VERB + CHALLENGE

be, present, represent
The demonstration represents a direct challenge to the new law

PREP

~ to
a legal challenge to the president's power

ADJ

leadership, title
his title challenge to the heavyweight champion

VERB + CHALLENGE

issue, mount
plans to mount a leadership challenge within the party
accept, take up
I accepted his challenge to a game of chess
beat off, fight off
Our team will have to fight off the challenge from better trained teams

PREP

~ from
a challenge from the other political party

ADV

directly
The newspaper was directly challenging the government's legitimacy
seriously
effectively
She was effectively challenging the whole basis on which society was run
successfully
The story was completely untrue and was successfully challenged in court

PREP

on
She challenged him on his old-fashioned views

ADV

seriously
No one has seriously challenged the champion
successfully, unsuccessfully

PREP

for
She was poised to challenge for the party leadership
to
The count challenged him to a duel