Each jurisdiction sets its own assessment method, frequency, and rate. US counties reassess every 1-5 years; Singapore reassesses annually based on the Annual Value (the rent the property could fetch). Some jurisdictions have a separate "vacant" surcharge to penalise empty homes (Vancouver, Singapore, Hong Kong).
Non-residents are usually taxed at the same rate as residents on the property itself, but may face additional acquisition taxes (US FIRPTA on disposal; Singapore Additional Buyer's Stamp Duty up to 65%; Hong Kong Buyer's Stamp Duty 15%).
Estate / inheritance treatment varies wildly — UK applies IHT to UK-situated property regardless of the deceased's domicile; the US has FIRPTA on transfer. International estate planning is jurisdiction-by-jurisdiction.