There are 28 essential micronutrients (vitamins & minerals). Included in this group is a list of 8 essential trace minerals. Of these 8, perhaps none is as powerful (or misunderstood) as iodine...
IODINE, THYROID & METABOLISM
The human body needs iodine to produce thyroid hormones (including T4 and the more metabolically active T3), which play a major role in overall metabolic health. Adults generally carry between 15-20mg of iodine in their body, 70-80% of which is stored in the thyroid gland.
In children, iodine deficiency can lead to impaired growth and cognitive development.
In adults, iodine deficiency is often an underlying cause of hypothyroidism, which commonly leads to low energy, weakness, weight gain, hair thinning and cognitive impairment. [1-4]
ASSESSING THYROID HEALTH
When it comes to assessing the function of the thyroid gland, I prefer looking at free T3 levels (versus the more standard TSH and less standard free T4). Free T3 is the best indicator of how much bioactive thyroid hormone is circulating in the body, whereas TSH is not an active thyroid hormone but rather a thyroid signaling hormone released from the pituitary gland (it's relatively common for people to have "normal" TSH but sub-optimal free T3 levels).
IODINE IN FOOD
While the RDA for iodine is 150mcg, therapeutic doses for correcting an under-functioning thyroid gland are several times this amount, often 1-50mg/day (7-70 times the RDA). One of the problems here is that an upper tolerable limit of 1mg (or 1000mcg) has been set, which discourages many from consuming iodine in amounts that will actually move the needle when it comes to thyroid and metabolic health.
Like many essential vitamins and minerals, obtaining truly therapeutic doses from food alone is next to impossible (which is why I often recommend iodine supplementation). For instance, aside from edible kelp (which can contain ~20mg iodine in 1/3 cup but isn't typically found in the American diet), significant sources of dietary iodine include iodized salt (150mcg in 1/2 tsp) and whitefish like cod or haddock (150mcg in 4oz). Indeed, it was widespread goiter caused by iodine deficiency in the "goiter belt" that led to the iodization of salt in the U.S. in 1924. The goiter belt includes the Great Lakes area (especially Michigan & Wisconsin), upper Midwest (especially Montana & Idaho) and the Pacific Northwest (inland Oregon & Washington).
For those with an under-functioning thyroid (free T3 levels of <3 pg/mL) I generally recommend iodine supplement dosing based on free T3 levels.
* For those with free T3 levels <2 pg/mL, a daily iodine dose of 12.5 to 50mg may be most therapeutic.
* For those with free T3 levels between 2 and 3, a dose of 6.25-12.5mg/day may be most beneficial.
* And for those with free T3 levels between 3 to 4.5 (considered optimal by many integrative providers), a maintenance dose of 1-3mg/day of iodine may be best.
Despite most of mainstream medicine cautioning against iodine supplementation >1mg (1000mcg) a day, research shows that most individuals tolerate high dietary intakes of iodine remarkably well. 
COMPANION NUTRIENTS & CONTRAINDICATIONS
Companion nutrients for thyroid health include iron, selenium & zinc. I generally do not recommend selenium supplementation for those with hypothyroidism, as even relatively low doses of selenium (100mcg/day) can sometimes slow thyroid activity.
Iodine supplementation like that mentioned above (1-50mg/day) may be contraindicated for those with Grave's disease or hyperthyroidism. Iodine supplementation can be beneficial for those with Hashimoto's Thyroiditis (HT), but more caution should be used with higher doses, as high dose iodine can damage the thyroid gland when the gland is already inflamed, as is the case with HT.
1 https://pubmed.ncbi.nlm.nih.gov/30891786/ (2019; Iodine is essential for thyroid hormone synthesis)
2 www.ncbi.nlm.nih.gov/pmc/articles/PMC5004493/ (2016; “Pregnant women, infants & young children are particularly vulnerable to the effects of iodine deficiency because of the importance of thyroid hormone for normal neurodevelopment”)
3 www.thelancet.com/journals/landia/article/PIIS2213-8587(14)70225-6/fulltext (2015; “Iodine deficiency early in life impairs cognition and growth, but iodine status is also a key determinant of thyroid disorders in adults.)
4 www.ncbi.nlm.nih.gov/pmc/articles/PMC4192807/ (2014; “Iodine is a micronutrient essential for the production of thyroid hormones. Iodine deficiency is the most common cause of preventable mental impairment worldwide.)
5 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4049553/ (2014; "Most individuals tolerate high dietary intakes of iodine remarkably well.")