I applied online. The process took 2 weeks. I interviewed at Barclays (London, England) in Nov 2009
Interview
First, a phone interview mostly based on my personal background (personality test) along with classical questions such as: Why Barcap ? Why did you choose to study math ? Why do you want to work on a trading desk ?
Then the assessment center in London: one full day of 1:1 interviews (4 in my case) with operationals from different desks + a trading game (1h30).
Finally, the "final round": got interviewed by a full desk (3 traders). They asked me a lot of technical questions and checked my quantitative background, they also explained to me what products they trade.
Interview questions [1]
Question 1
Write a quasi-algorithm that computes the implicit volatility (i.e. numerically inverts the Black-Scholes formula) with the Newton-Raphson method.