With Proof-of-Stake (PoS) a blockchain is secured not by spending an external resource such as electricity but by using value internal to the chain itself. The promise of higher security at a lower cost is what also drives Ethereum to plan a move away from Proof-of-Work to PoS in the future.
Ethereum researcher Vlad Zamfir, who leads their effort in the complex search for the optimal PoS consensus system joined us for an in-depth discussion of the challenges of PoS, the approach Casper is taking and what consensus in Ethereum land could look like in the future.
Topics covered in this episode:

How he became interested in consensus and Proof-of-Stake (PoS)
Why Ethereum plans to switch to the PoS systems Casper in the future
What the Long-Range Attack and Nothing-at-Stake problems are and how Casper addresses them
How a betting mechanism is used to get validators to reach consensus
What centralization pressures exist for validators and what operating a validator will look like
The role of security deposits in Casper
The difference between Tendermint and Casper
Whether forks create big UI/UX issues for Casper
Why Casper is very light client friendly

Episode links:

Introducing Casper - Ethereum Blog
Review of Casper, Ethereum’s proposed Proof of Stake Algorithm
Casper Protocol Specification
Slasher, Ghost and Other Developments in Proof-of-Stake
Epicenter Bitcoin Episode 58 with Vitalik Buterin on Proof-of-Stake

This episode is hosted by Brian Fabian Crain. Show notes and listening options: epicenter.tv/105