acute, big, enormous, grave, great, huge, important, major, serious, significant
Our greatest problem is the lack of funds.

global
The traffic in illegal drugs is a global problem.

terrible
The accident poses a terrible problem for the family.

real
perceived
little, minor, petty, slight
complex, complicated, difficult, knotty, thorny, tough
growing
basic, central, fundamental, key, main, major, number-one (esp. AmE)
Access to capital is often the number-one problem for many entrepreneurs.

underlying
the underlying problem that's causing your high blood pressure

annoying, vexing (esp. AmE)
common
pressing, urgent
unforeseen
Unforeseen problems often arise.

immediate
possible, potential
Fortunately, it's easy to avoid any potential problems.

insoluble, insuperable (formal), insurmountable (formal), intractable (formal)
Depression is a natural feeling if your problems seem intractable.

unresolved, unsolved
The role of the sun in climate change is still a big unsolved problem.

age-old, long-standing, long-term, perennial
chronic, ongoing, persistent, recurring
inherent
the inherent problems of merging two very different companies

logistical, practical
mechanical, technical
systemic
Systemic security problems have been identified.

attitude, behaviour/behavior, behavioural/behavioral, developmental, emotional, mental, mental-health, psychiatric, psychological
His teachers say he has an attitude problem.

family, personal
Her new job had taken her mind off her family problems for a while.

communication
We had communication problems.

fertility, health, medical, physical, sexual, sleep
back, heart, knee
alcohol, drink (BrE), drinking (AmE), drug, gambling, substance-abuse
She had serious substance abuse problems with both cocaine and heroin.

social
housing
economic, financial, money
They sold their car to ease their financial problems.

environmental
political
legal
marital, marriage
ethical, moral
Most people can see the ethical problem with accepting such an offer.

host, set
We're faced with a whole host of new problems.
an elegant solution to a very complex set of problems

be, pose, present (sb with), remain
Inadequate resources pose a problem for all members of staff.

have
develop
He developed a drinking problem.

bring, cause, create, pose
Success brings its own problems.
Staff shortages cause problems for the organization.

complicate, compound
be beset with, be confronted by, be confronted with, be dogged by (esp. BrE), be faced with, be fraught with, confront, encounter, experience, face, run into, suffer
He has been faced with all sorts of problems in his new job.
The plan has been fraught with problems from the start.

battle
an important step in battling the terrorist problem

attribute, blame
the problems attributed to capitalism
They blame the problem on the new prescription drug law.

raise
She raised the problem of falling sales at the last meeting.

see
He doesn't really see the problem.

define
acknowledge, admit, recognize
I'm glad you finally admitted your problem.

understand
He doesn't seem to understand my problem.

anticipate, foresee
I don't anticipate any future problems in that regard.

detect, discover, identify, isolate, pinpoint, spot
indicate, point out
These symptoms may indicate a serious problem.

assess, examine, investigate, study
They created a task force to study this problem.

diagnose, figure out (esp. AmE), work out
consider, debate, discuss, look at, look into
describe, frame (esp. AmE)
Framing the problem is an important step.

address, approach, attack, combat, come to grips with, counter, get to grips with, grapple with, handle, manage, tackle
The next meeting will address the problem of obesity.

illustrate
This illustrates another potential problem.

highlight, underscore (esp. AmE)
This underscores the biggest problem with electronic voting.

mask
All the anti-depressant does is mask the problem.

avoid, circumvent, find a way around, find a way round (esp. BrE), get around, get round (esp. BrE), prevent, sidestep
ignore
overlook
For years I've tried to overlook this problem.

forget
I forgot my problems for a moment.

clear up, correct, cure, deal with, eliminate, fix (esp. AmE), iron out, overcome, rectify, remedy, repair, resolve, settle, solve, sort out, troubleshoot
He had to undergo surgery to cure the problem with his knee.

alleviate, ease, minimize, mitigate, reduce, relieve, simplify
aggravate, exacerbate, exaggerate, magnify, worsen
analyse/analyze, explore

arise, come up, crop up, emerge, occur, surface
problems arising from poor ventilation

exist
begin, originate
No one ever asked why or how the problem originated.

persist, remain
If the problem persists you should see a doctor.
The basic problem remains the lack of available housing.

afflict sb, beset sb, confront sb, face sb, plague sb
lie in sth
The problem lies in the lack of communication between managers and staff.
Therein lies the problem.

result from sth, stem from sth
a problem resulting from technical inadequacy

area, spot
behaviour/behavior
child
drinker, gambler
One out of every five people is a problem drinker.

drinking, gambling
a new approach to problem drinking

page (BrE) (= in a magazine, containing letters about readers' problems)

problem about
I didn't imagine there would be a problem about getting tickets.

problem for
The rail strike is a problem for all commuters.

problem of
the problem of poverty

problem with
Do you have a problem with her?

an approach to a problem
the crux of the problem, the heart of the problem, the root of the problem
We need to get to the root of the problem before we can solve it.

the answer to a problem, a remedy to a problem, a solution to a problem
He believes he may have found the answer to his problem.
He believes he may have found a solution to the problem.

the scale of a problem

complicated, difficult
easy, simple
math (AmE), mathematical, maths (BrE)
the ability to solve simple mathematical problems

do, find the answer to, solve, work out
I have five problems to do for homework.

set (AmE)