Upcoming expiration dates for monthly VIX options and futures—they expire at market open on the same days can be found here. The settlement price is not the same as the VIX open price. The settlement price is listed under the VRO ticker and reflects the result of a process (HOSS) managed by the CBOE. The settlement process involves actual trade prices, not the mid-price quotes used in the VIX calculation process so the ultimate settlement price can be significantly different from the VIX open price.
The last day of trading for expiring VIX options is the end of regular trading on the day before (typically Tuesday). Expiring VIX futures on the other hand trade extended-hours trading until 7:00 AM ET on the day of expiration (typically Wednesday).
See this post for thirteen things you should know about trading VIX options.
The underlying security for VIX options is not the CBOE’s VIX index, in fact, since it is cash settled and can’t be exercised before expiration it doesn’t have an official underlying security. However, it turns out that the volatility futures expiring on the same date are a good approximation to the underlying for computing Greeks, etc. The CBOE’s Future exchange site has delayed quotes on VIX futures. The symbology is not obvious, for example, the ticker for Dec 2019 futures would vix/z9. The symbol is built up by taking “vix/” plus the month code (month codes are listed here). plus the last digit of the year (9 for 2019).
The VIX and volatility futures do approximate each other on their expiration date (see below for the discussion on VRO), but otherwise the volatility futures can be lower or higher than the VIX. VIX central is a very useful website that not only gives the VIX futures delayed quotes, but also shows the term structure—a graph of the VIX Futures for the various expiration dates vs time. The VIX central site also has historical VIX Futures data which can be compared to the term structure of the CBOE”s constant maturity indexes: VIX9D, VIX, VIX3M, and VIX6M which show 9, 30, 93, and 180-day expectations of volatility.
You can also get a good estimate for the volatility futures prices by looking at the $10 VIX call for the corresponding option series. For a given set of options if you split the bid/ask price of this deep in the money option, and add 10 you are pretty close to what the VIX futures for that expiration are trading at. For example, if the $10 call is at 8.50 bid, 8.90 ask, then split the difference to get 8.70, and add 10 to get 18.70. This is the approximate VIX futures price that underly those options. Volatility Exchange Traded products (e.g, VXX, VXZ, ZIV, UVXY, SVXY, TVIX) are based on various uses/mixtures of the monthly futures. See Volatility Tickers for a full list.
The exercise/settlement values on the expiration date are not the opening values of the VIX / RVX index, but rather their special opening quote values. These quotes have their own symbol and are printed sometime after opening—usually a few minutes after, but it can take an hour or two to achieve a settlement. The VIX settlement value ticker is VRO (Yahoo ^VRO, Schwab $VRO), and RSL for the Russell Volatility index.
Source: OCC and CBOE option expiration calendars
For a spreadsheet calculator for all historical expiration days see this CBOE tool.