We've been warned about the potential risks of cell phone use due to radiation for ages, but to date, there hasn't been definitive information published that would warrant some sort of formal government or industry action. Nothing changes with that today, but California's Department of Public Health has deemed the risks to be high enough to issue a warning so that perhaps some users won't use these devices as much, as well as get out of the habit of regularly keeping them close to our bodies.
The CDPH admits that the "science is still evolving", so again, there's no reason for immediate alarm here, but it goes on to say that many public health professionals are growing concerned about the constant exposure we're subjecting our bodies to. The emissions from our smartphones may be at relatively low energy levels, but we need to think long-term.
HotHardware's Dave Altavilla, before the onset of hand-melting energy emissions
Because the energy emissions generated through phones are modest in the grand scheme, few have been truly concerned about their effects on our bodies. However, those who tend to use their phones constantly nowadays likely didn't use a phone nearly as much at all a decade ago. With our increasing dependence on these mobile devices, some industry professionals are starting to wonder if we should be looking at this issue more closely.
California's Department of Public Health isn't alone in this thinking; in 2015, Connecticut's DPH likewise issued warnings. This is despite phone manufacturers needing to adhere to safe exposure limits. In the worst case, safe exposure may be light usage; certainly not the kind of usage typical of today's power users, along with the trend of extensive social sharing.
This may sound completely impractical, but California's DPH recommends not keeping a phone in your pocket, to restrict the amount of time it's pushed against your head, and to kick it out of bed. For sanity reasons, the latter suggestion may be a good one anyway. Even Facebook has had similar ideas.
It's important to emphasize that there's no reason for alarm right now; this is a warning, nothing more. The fact that we've gone so long without major issues being revealed gives confidence that the overall issue will should minor, but that doesn't mean that will remain the case for the long haul. Hopefully if there are indeed specific health risks, they will be discovered sooner than later. At this point, though, it seems likely that many will continue to go on with their digitally connected day as normal.