McKinsey & Company (a prominent consulting firm) has released a report on the application of blockchain technology to the insurance industry.
The second half of the report is a great overview of some of the projects being developed by blockchain startups: Tradle (built on Bitcoin), InsureETH (P2P insurance), Dynamis (P2P insurance), and Blockverify (anti-counterfeiting). Although curiously the report doesn't mention Ethereum, the software platform upon which most of these startups are built (and which itself is under heavy development).
The first half of the report is a good overview of what blockchains are. My only quibble with their overview is that blockchains aren't necessarily "immutable" in the way they describe. Blockchain blocks are only immutable so long as there is consensus (amongst the people running the software that creates the blockchain) that the blockchain should remain immutable. The Ethereum developers are debating making changes to the Ethereum software that would alter past transactions connected to "The DAO" (i.e. a "hard fork").
Blockchains aren't magic. They exist due to software and software can be changed. The key to understanding why blockchain date is almost always immutable in practice is understanding how the larger system works, including the economic incentives for mining.
I would recommend that insurance companies (or anyone else) looking into blockchain solutions ask questions about the underlying blockchain. Is it the Bitcoin blockchain? Ethereum? A private system? Each of these have very different characteristics that bubble up to the software (such as a smart contract) running on top of the blockchain.
An excellent word of caution near the end of the report:
Blockchain is a technology ready for exploration by insurers. But its exploitation is still a long way off..