MSM, also known as methylsulfonylmethane, is a naturally occurring compound that contains sulfur. The sulfur in MSM plays a crucial role in the formation of collagen and glucosamine, both of which are vital for healthy bones and joints. Research has also shown that MSM has anti-inflammatory and antioxidant effects, which makes it relatively easy to see why there have been a lot of studies around MSM's potential benefits for joint health.
It should be noted however, that a lot of the highest quality trials on MSM have tested it alongside glucosamine and placebos, with MSM often coming second to glucosamine, but showing increased efficacy when they are used together.
There have been a few areas in which MSM has been effective in terms of studies, mostly this has been around mobility and swelling although there is also some evidnce to suggest it can help manage pain, there are other natural compounds that target pain more effectively.
It's also worth noting that there is evidence to suggest that MSM can be used either topically or orally and still benefit joint conditions, with of course most of the research in relation to MSM coming from arthritis studies specifically.
Topically there are a lot of anecdotal claims that MSM cream seems to be beneficial for arthritis of the hands.
MSM and Improving Joint Mobility
MSM could also be more beneficial when combined with other well known joint supplements such as glucosamine, for example in a recent a clinical trial involving individuals with knee osteoarthritis, participants were given various treatments, including glucosamine, MSM, a combination of both, or a placebo. The results showed that both MSM and glucosamine significantly improved joint pain and swelling compared to the placebo group. Interestingly, the combination of MSM and glucosamine yielded the most significant reduction in both pain and swelling, as well as improved functional ability in the joints. 
On tops of this MSM has shown promise in reducing pain and stiffness in the lower back. A study involving 32 individuals with lower back pain found that MSM supplementation combined with glucosamine significantly reduced lumbar stiffness and pain upon movement, leading to an improved quality of life. 
And another often cited trial focused on individuals with osteoarthritis related knee pain. The participants were divided into two groups, with one group receiving MSM capsules and the other group receiving a placebo. The study found that only 25% of participants in the MSM group experienced some improvement in pain and physical function, while there was no significant difference in stiffness compared to the placebo group. 
MSM and Inflammation
In the aforementioned study, comparing glucosamine, placebos and MSM, the osteoarthritis patients demonstrated that both MSM and glucosamine supplementation led to a significant reduction in joint swelling compared to the placebo. However, glucosamine appeared to have a more pronounced effect in reducing swelling. When MSM and glucosamine were combined, the reduction in swelling was even more significant than when either supplement was used alone. There have also been studies combining MSM and boswellic acid, which again resulted in a greater impact. 
Specifically MSM has been shown to inhibit the release of inflammatory cytokines (the thing that causes the body to swell) and reduce the production of molecules associated with inflammation. This has been shown outside of joint conditions as well as in studies conducted on arhritis patients, for example a study conducted on stomach ulcers demonstrated that MSM supplementation reduced inflammation, further evidencing that it does in fact reduce swelling. 
MSM Cream, Does MSM Work For Joints Topically
MSM has also been shown to reduce swelling and inflammation when applied topically, it does also seem to be good for the skin in numerous capacities, everything from exhema to psoriasis. This does suggest it could be particularly benefitial for arthritic psoriasis, although there are limited direct studies.
One of the few direct studies done on MSM cream looked at the effects of three preparations. These included MSM cream, HA (hyaluronic acid), and MSM + HA on swelling. The results demonstrated that MSM + HA reduced the bodies production of inflammatory markers such as inducible nitric oxide synthase (iNOS) and prostaglandin E2 (PGE2). This combination resulted in increased cell and tendon healing. 
So the jury is a little out on how well MSM creams treat joint pain, beyond reducing inflammation.
MSM in Healthy Populations
Another study published in the Journal of the International Society of Sports Nutrition investigated the effects of MSM supplementation on muscle and joint pain as a result of exercise. Participants in the study were given either MSM or a placebo for 21 days before and two days after a half marathon race. The results showed that MSM supplements reduced muscle and joint pain compared to the placebo. It wasn't by a huge amount, but it was noticable, which is further evidence for it's use. 
MSM Side Effects
Short-term use of MSM supplements appears to be well-tolerated, even at high doses. Clinical trials have used daily doses ranging from 1,500 mg to 2,600 mg for up to three months without significant adverse effects. Mild side effects, such as gastrointestinal discomfort, have been reported, but no serious long-term side effects have been identified.
MSM supplements have been reported to enhance the effects of glucosamine in reducing pain and swelling in osteoarthritis. However, there are no well-known interactions between MSM and medications, herbs, supplements, or foods.
There is also some evidence to suggest that MSM should be avoided if you have a pitted edema (a type of fluid build up) so it may not be suitable for all joint issues although when combined with other compounds it can have a positive effect, making this a slightly complicated issue. 
How Long Does MSM Take to Work?
Unfortunately MSM does take time to build up in the system and isn't one of the faster acting pain relieving supplements. We are looking at a period of at least 2 weeks to feel it's full effects.
When applied topically it can have a much faster effect on swelling and skin damage, but once again we are talking about several weeks consistent use for optimal results.
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5 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5372953/
6 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5521097/
7 - https://pubmed.ncbi.nlm.nih.gov/21366964/