As you may know, I have been in the process of moving to the UK. I'm happy to say I have completed the initial stage of that process, and I arrived in Biggleswade last week. Yesterday I picked up my BRP, a biometric residence permit. To my delight, the card is pink, white, and blue.

I came here on a spousal visa, it is a three step process: First you are granted Leave to remain (33 months), then further leave to remain (30 months), and finally indefinite leave to remain. When I reach indefinite leave to remain at approximately the 5 year mark, I'm eligible to apply for citizenship.
The requirements for the initial visa are a sponsor, proof of suitable accommodation, and proof of financial eligibility. You are also required to pay an IHS fee to the NHS. The current criteria for finances are that the UK partner must make at least £18,600 per annum, or alternatively, the US partner must have £68,500 in savings, held for a minimum of six months.
The current application fees ( they are adjusted annually) for the first visa are:
£1500 Visa application
£1200 IHS fee
£650 Priority (30 day) processing fee, this is optional.
This totalled up to $4,321 for us.
The fees for the second visa are currently:
£1,000 Visa application
£1,000 IHS fee
£650 Priority processing fee, this is optional.
The fees for the indefinite leave to remain (settlement) visa are currently:
£2389
£650 Priority processing fee, this is optional.
For all of the steps above, you have to prove the relationship, accommodation, and financial eligibility requirements.