The tax consequences for such a move are the same as a conversion from a traditional IRA to a Roth IRA. You'll have to treat pre-tax contributions as taxable income in the year in which you convert to the Roth IRA, but any after-tax contributions aren't required to be included in taxable income.
What you can't roll over to a Roth IRA
Finally, there's one category of retirement account that's not eligible for rollover to your personal Roth IRA: an inherited IRA. If you inherit a traditional IRA from a non-spouse, you're stuck with the traditional nature of that retirement account under current law. If you inherit a Roth IRA from a non-spouse, you'll need to open an Inherited Roth IRA and plan to take required minimum distributions (RMDs) over a 10-year period (assuming you inherited the account after Jan. 1, 2020; if it was before then, you are able to take RMDs over your lifetime).
The only exception is if you're the spouse of the deceased IRA holder, in which case you have the right to move inherited IRA assets into your own IRA. From there, you can then convert your own IRA to a Roth. However, as mentioned above, non-spouse beneficiaries don't have that option.
Chart of Roth IRA rollovers