Nine candidates remain in the race – three have dropped out – to take over from Mr Ban on January 1.
And for the first time ever, the race to succeed him is being played out, at least in theory, in the open.
The Secretary-General is chosen by the Security Council, but the candidates have been asked to make their pitch for the job. They set out their vision before the General Assembly, and answered questions from the representatives and those submitted via social media.
Custom dictates that the appointment rotates by region - hence the significant number of Eastern Europeans vying for the role. The US and UK have also been loud in calling for a woman to take the reins of the UN for the first time.
Although there is technically no limit to number of five-year terms a Secretary-General may serve, none so far has held office for more than two terms.
Here is a look at the 12 candidates who wanted to be the world's top diplomat, in order of preference from the most recent straw poll.
There is another straw poll on September 26 and the Security Council will move to coloured ballot papers – showing whether a candidate is likely to be vetoed by one of the five permanent members - for the first time in early October.