As of 2021, all of the below wave energy based treatments are almost exclusively used to treat armpit sweating. Some doctors and researchers are using these newer technologies to treat excessive hand, feet and facial sweating treatment, but I would not risk being a guinea pig till more results and studies come out. The skin on your palms and soles is a lot thicker than in the armpit region, and the palms and soles both have far more sweat glands than the armpits. You also likely do not want to cause any damage to your facial skin.
Make sure to also see my page on extra strength antiperspirants to treat your underarm sweating.
This treatments has become so popular in recent years, that I have a separate page on this site that covers miraDry treatment in great detail. Below are several videos that give you a good overview of the procedure:
SweatX is a proprietary cryo-thermal therapy laser treatment from Alma Lasers. It claims to stop excessive armpit hyperhidrosis and bromhidrosis (aka smelly sweating). It seems like you need 4 treatments per area (price averages $500 per session), and the results last for 9 months (but potentially much longer). Also see Harmony XL Pro cryo-thermal sweat treatment.
Radiofrequency (RF) microneedling based treatments for excessive armpit sweating have become very popular recently. A 2016 study found that the combination of RF and fractional microneedle technology (aka fractional microneedle radiofrequency -- FMR) reduces axillary hyperhidrosis. There are numerous devices that can treat excessive sweating with radio frequency. On YouTube, some are even used to treat facial sweating, although I would be cautious before attempting to treat that area of the body.
A new nonsurgical ultrasound therapy called Ulthera has shown some promising results since 2011 and was undergoing FDA clinical trials in 2012 and 2013, but as of 2014, not much has been reported on the final results. If successful, this could become the most popular treatment, since ultrasound is less dangerous in comparison to electromagnetic radiation (lasers, microwave, radiofrequency etc...). It should be noted that even electromagnetic radiation is generally very safe at the lower doses that are used in treating axillary sweating, but many people and scientists are still concerned about potential long-term side effects since we are constantly exposed to so many waves these days (microwaves, GPS and cell phone signals, wifi signals, x-rays, radio waves and more).
"Graydwarf " on the forums on this site has a super useful thread on various treatments that he has tried, and one of those is Ultherapy. See his updates to his first post from July 2014 and onwards for his experiences with Ultherapy.
A number of doctors have been treating hyperhidrosis using various lasers in recent years. Perhaps the most well known of these are Dr. Whiteley (LSA -- laser sweat ablation) in the UK and Dr. Nielsen (SDLA -- subdermal laser ablation) in the US. Both these doctors seem to have their own proprietary technologies and techniques. Dr. Whiteley has trained a few other doctors to use his technique.
However, in recent years, Cynosure's PrecisionTx laser technology has garnered significant positive reviews when used to treat excessive armpit sweating, and many doctors are purchasing it, especially in the US. The unique aspect of this laser device is that after a very thin cannula with proprietary SideLaze fiber is inserted under the skin, laser energy is directed upwards towards the undersurface of the skin, targeting sweat glads and hair follicles there. This reverse counter-intuitive application of a laser limits potential damage to deeper areas underneath the skin surface as is often a risk with most other cosmetic lasers that are used on the surface of the skin rather than underneath it.
Video from Dr. Barbara Padilla in Connecticut:
Another laser option is Fotona's XP line of Nd:YAG lasers to to treat axillary hyperhidrosis. Their procedure takes around one hour with the use of a local anesthetic.