Depends on your definition of "modern".
The iPhone wasn't the first to support apps (Windows Mobile / CE handsets had been around for a while, but they weren't nice to use as a "phone". Also plenty of feature phones, eg most of Sony Ericsson's pre-Android range- supported apps too).
If you meant "the first smart-phone form-factor", then there were Nokia and sony handsets long before the iPhone. But they weren't all that great from many of the accounts I heard (which always put me off buying one). Blackberry and Palm (remember them) also had some great offerings for their era too.
If you meant the "first with capacitive touch screen", then LG beat Apple to the market with an iPhone-like device by a few months.
However Apple's iPhone is still the handset we all remember as being the groundbreaker. I don't know if that's because Apple PR team have done a wonderful job rewriting history; or because Apple happened to build the most successful product of that era that it made other products before it seem forgettable. Maybe a bit of both. But in any case, I think if you want to credit the iPhone for it's importance in history then it's only fair to credit the numerous other handsets which preceded it and pioneered the various different technologies and paradigms that Apple then went on and merge together so effectively.