There are 3 basic categories of trading: discretionary, market making, and quantitative. Quantitative trading, algorithmic trading, and black/gray box trading are very similar and sometimes used interchangeably. For those positions, employers generally want an extremely strong quantitative background ranging from an undergraduate math degree to a masters in engineering. For market making and discretionary trading, there are no specific qualifications. A quantitative background is always respected, but generally not required. Specific knowledge like accounting or finance is generally considered useless.