From what I can tell a majority of quant roles at banks are programmers with really good maths ability and financial product knowledge. There is an emphasis on stochastic calculus here. The skill-sets of these guys are truly impressive. One of the math finance post-docs at my uni said that out of his 3-man maths/finance phd graduating class, 2 guys went to banks and he went into academia, and that his 2 friends describe themselves as "glorified programmers". These guys all need C++.
Another type of quant is risk guys, who mainly need good VBA (the head of risk at optiver was a nuclear scientist, but he thinks the role isn't challenging). Some risk roles (compliance risk, qualitative credit risk) is not quantitative. Market risk is heavily quantitative. For example, quantitative risk consulting at an advisory firm (typically a "big 4" accounting firm) is all market risk stuff (also some quantiattive credit risk). You're designing hedging strategies over a broad array of industries, pricing financial derivatives and all sorts of fancy stuff. Their clients are almost all the big banks as well as large companies. At KPMG there is only 1 guy that uses R, which is completely sad considering they're the biggest in the market. They're mainly VBA.
Retail banks also have quant teams. There's a small, 5 man team at Australia's largest retail bank that does economic/demand modelling. They talked to me specifically about probit, how I would handle gigantic amounts of possible independent variables, and the use of economic factors, so I guess it's heavily econometric. They have 2 PhDs and 1 actuary on the team at least so would be quite technical. They use SAS and SQL with some Excel. Can't even install R on the computer unless your "cost centre" ("center" in American) pays $280 to the IT team to do some virus check or something. Very sad!
But onto trading:
I've interviewed for the quantitative arbitrage desk at Optiver but didn't get it. It's definitely the hardest and most competitive type of quant role to get. Their starting salary is 100K + bonus which is just absurd for a 22 year old working 9-5. However apparently the attrition rate is very large (you're fired if you lose money). They said that everyone was expected to know how to code but being a very strong programmer wasn't essential. They said I would be building prototype strategies in R and Python and then we'd hand it to put it to programmers to put it into C++. They wouldn't tell me what their strategies were though. I know they do high frequency trading but I doubt I would've been going there. I probably would've been automating the market making of options markets, where your goal is to provide the most profitable bid-ask spread while keeping your "Greeks" in check (I think this is the case because most of the testing was on options knowledge).
Others like Regal fund management uses quantitative strategies on a longer term horizon. I'm not sure of what strategies they use (I know long term volume and momentum factors) -- perhaps a factor model, I wouldn't be surprised. Definitely a completely different universe to high frequency trading or options market making.
Another aspect of quant work in a fund might be quantitative portfolio management. e.g. applying bootstrapping/resampling techniques to construct mean-variance (with respect to, perhaps, any form of utility function as the objective function) efficient portfolios. Constructing Black Litterman portfolios. Standard portfolio stuff that requires good quantitative skills. Lots of finance academics get consulting gigs in this area.
A related universe is quantitative investment consulting products, where your clients are pension funds, insurance companies, etc. Here actuarial type models are important as you always need to make sure you have enough to pay the grannies and the liability claims ("asset-liability modelling"). In Australia there might be 15-20 guys that have this job. One of the two biggest investment consultants outsource all this to their UK office. The other biggest one doesn't, their team is about 5 guys. There's another semi-quant team that sets long-horizon return expectations. I'm not sure exactly the models they use but I heard "Markov-switching" from a principal so it sounds decent. They have an engineer and a computer scientist as well as finance guys. But another one said my 8GB thesis dataset was "very large" so they probably work mostly with daily frequency data, maybe even a longer horizon. They only use VBA and Matlab, which is more evidence for daily frequency data. But they want the untested new-comers to learn VBA because they don't want to fork out for the expensive license.
Yet another area is co-integration trading. I don't know too much about this area. I know that the largest quantitative fund in Australia uses co-integration trading. The director of the quantitative finance masters at my university helped to set up their strategy. Also a friend who's doing his thesis on co-integration trading over brownian motions met a guy who's starting a 500m co-integration fund. Interesting factoid is that he thinks academia is really far behind the strategies that he's using/built surrounding co-integration (could just be ego). It was something to do with time-variation/structural change in the time series that academics haven't handled well yet.
I also know that a professor got snapped up by Barclays global investors after he published a paper on using machine learning algorithms to construct a buy-hold strategy that delivered around 250% returns over 8 years. So maybe there's room for that stuff as well. However he was a professor of economics so they might not have gotten him for this (also post transaction cost the strategy wasn't great).
There's also fixed income trading/portfolio management. I don't know much about this. I do know that someone got one of the only quantitative fixed income graduate jobs in Australia because they did absurdly well in their mathematics degree (combined with finance), so there's probably quantitative ability needed. They said the role was all VBA. Definitely those that trade the yield curve with different strategies (e.g. surfing the curve, barbells, etc) will need to have very competent statistical abilities. Splines, interpolations and numerical stuff comes into it a lot. Also forecasting changes in all the different derivatives along the Taylor's expansion would be a very difficult task ....
ANOTHER area is quantitative portfolio insurance. It's when, as the market tanks, you sell a proportion of the portfolio and buy risk free bonds. The product is constructed such that the return at maturity is never less than some tiny positive amount. You need good models to avoid sterilization (early convergence to the cushion line) and also to ensure that the probability of defaulting (going below the safety line) is something like some N-sigma event, where N is agreed upon with the institution that purcahsed the product..
That said, if you don't have an impressive resume (quantitative PhD maybe, or something else that makes you stand out) or don't have relevant experience, you're not going to get in. Best you'll be doing is trader's assistant work in VBA.
If you do happen to get an interview, you will almost surely be asked very difficult numerical/probability brain teasers. E.G. at IMC you are asked 40 questions in 30 minutes like and you have to give the exact correct solution without ANY working (it's not multiple choice either) and no alterations are allowed after you write in the answer. Only 1 guy in the Australian office has gotten 100%. I got 30/40 after a lot of practice with this R problem generator I made, but was blitzed by this straight A electrical engineering student across the table from me. There's some serious geniuses that you have to compete with at these trading places. They take 1/2 out of about 1000 applications each year. Last year they took 0 out of a similar number of applicants. At Optiver they bombard you with more, easier questions in less time, but everyone I saw on my table failed that one. I only know one guy that got this job and he went to the IMO. At SIG they ask you on the spot questions where you have to apply binomial probability to determine the solution. At Westpac financial markets (Fixed income trading) they asked about conditional dice probability - fine if you have a pen and paper and can think about the sample spaces and stuff but VERY hard in your head.