There are 4 ways to make a fan compatible with SmartThings.
- Replace the wall switch
Wire the fan to a wall switch and replace the switch with a SmartThings-compatible one that is also compatible with a fan motor.
This has been a popular solution and there are quite a few options. Some can also control lights on the fan, some require a separate light switch, it just depends on the model of the fan and the switch. The Zooz mentioned above falls into this group. See the community FAQ on this approach. (The title mentions Alexa, but the same models work with ST without a smart speaker.)
Note that many of these require custom groovy code which will stop working in a few months when the SmartThings IDE goes away. So do further research before making a big investment. Zooz and Inovelli have already committed to updating for the new platform. Lutron and Bond already use a cloud to cloud integration which is not affected by the change.
FAQ: 2020 Ceiling Fan and Dimmer light wall mount control compatible with SmartThings and Alexa?
- Mimic an Existing Remote
Buy a fan with its own button remote, then add a SmartThings compatible device that works the way the remote does.
Bond’s entire design is based on this idea and works well with many different fans, although the exact features you get vary from model to model.
This option has become increasingly popular, particularly since they now have a partnership with Home Depot for several of the Home Depot brands. And Because Bond is simulating the fan’s own remote, no extra wiring is required. 
Bond has a manufacturer-provided cloud to cloud integration available through the SmartThings app. No custom code required, and it should work after the IDE goes away.
It’s always possible that either company will drop support sometime, but that’s true with any device.
Bond as a company does have a history of overpromising on future features, so only buy them based on the features that are available now.
- Replace the controller in the fan canopy
Replace the fan’s own motor controller with one that works with SmartThings. This requires rewiring the motor in the fan canopy. How hard that is varies by model. It may also mean that any handheld remote that came with the fan no longer work, again, that varies by model.
This used to be a very popular option using a Zigbee device from Hampton Bay, but that device has now been discontinued and it always required custom code. Tuya and Sonoff both have some offerings in this device class, both are using custom code which has not yet been updated for the new platform.
- Buy a smart fan which comes with ST ready integration
There are only a few of these. Home Depot offers some models which have Bond built in: these use the same Bond integration as in 2) above.
Minka also makes a line with Bond built in:
You can find a few more of this type which are not using Bond, notably WAC (and their subsidiary Modern Forms), in the “add a device” section of the SmartThings app under Fans.
This category in the app mixes together devices of all four types mentioned in this post, so you’ll have to do some research. Remember that a brand being listed doesn’t mean all of its devices work with ST: usually it’s just a few specific models. So again, research. 
If you want a whole new fan that works with ST and does not require custom code, and that uses a remote instead of a wall switch, one of the bond options is probably the easiest. But if you’re open to having a wall switch, then there are more choices from option one above.