This is the next revolution in fintech according to investors
"Be in the city around lunchtime and stop the people walking around carrying big reams of paper - they're insurance brokers," says Pascal Bouvier, a partner at fintech venture capital firm Route66 Ventures and a fintech blogger.
Peer-to-peer lending is transforming loans; crowdfunding is shaking up investment; companies like Klarna and Adyen are changing the way we pay online and inventions like Apple Pay are transforming the way we pay in person; and the blockchain technology that underpins bitcoin has the potential to make banks themselves quicker and leaner.
But, despite all this, insurance firms are still working in much the same way they did 10, if not 20, years ago.
Bouvier says: "Insurance companies are in some ways less advanced than banks were and still are when it comes to data, machine learning, and all of that."
For investors like Bouvier, that's a big opportunity. Technology startups can help insurance companies do their jobs faster, better, and cheaper - or just do it better themselves. Either way, they'll likely make good money in the process.
He says: "All 4 of our last investments were in the insurance space. It's a space that's barely explored."
"We're just at the start of an insurance explosion here. I've seen more and more insurance companies in the US, Europe, and Asia getting started. I wouldn't be surprised if we tally the numbers on investment in insurance startups two years from now and it's massive."
Amy Nauiokas, founder and president of fintech investment firm Anthemis, told me something similar when we spoke earlier this year.
"Seeing some of the new data-driven risk management products that are coming out is quite interesting. We're watching that space really closely."
Anthemis' biggest success to date was in insurance, with Climate Corporation. The San Francisco company used weather data to offer insurance to farmers and was bought by agriculture giant Monsanto for $1.1 billion (£720 million) in 2013.
Several other VCs I've spoken to recently have said that, for the first time in years, insurance is suddenly 'hot.'
Just this week Google invested $32 million (£20.3 million) in Oscar, a health insurance startup in the US that is one of the most prominent companies looking to rethink the way insurance works.
Not only are investors keen, the insurance firms themselves want to be "disrupted." A new accelerator is launching in London next January specifically focused on insurance and backed by some of the biggest names in the industry - car insurer Admiral, German giant Allianz, and Lloyds Bank.
"Industry appetite is actually not something I was expecting from the insurance world," says Nektarios Liolios, the managing director of the programme, Startupbootcamp Insurance.
"There seems to be a lot of hunger. I think they recognise that the financial world is in the process of doing this and the insurance world is lagging behind."
There is a lot of opportunity for lean tech startups to work their magic. Liolios says: "We look at interesting new business models like peer-to-peer or the crowd, just like in the financial industry a few years ago. What is exciting is new risk models and underwriting. But then it's also more mundane things like back-office improvements, claims-processing improvements. A lot of it is around distribution and user experience."
But there's one big piece of the puzzle missing - the startups.
Liolios says: "Not many startups self-identify as insurance startups. If somebody has a big data analytics platform, they could sell it to the insurance industry and it could be really valuable. We feel it is our responsibility to alert them to that."
The accelerator programme was first announce in June and so far Startupbootcamp has had around 50 applications. Liolios says this is a good number and he would be "really happy" if it gets 300 applications in total by October's cut off.
Part of the idea of the programme is to encourage more insurance fintech startups to be created, not just to nuture those in existance.
Liolios says: "The industry is just so early. Models like Oscar, it's clearly a very good startup. You've got Friendsurance in Germany which was one of the first ones to make a name with the peer-to-peer aspect. There are glimpses into possibility, but it's too early."