If your flight lands or departs at an odd hour, don't worry too much. It's unlikely you will get stuck at the airport, as there is usually a reasonable method of transit available. Likewise, if your flight departs very early in the morning, there is usually an airport bus route nearby that starts service early enough. It just takes some planning, which we will discuss below.
The Airport Express usually starts around 5:30AM, and ends around midnight. To find accurate up-to-date timing, let's see how to check Naver maps:
Here are the most common situations:
In this case it would usually be best to search for an airport bus route that gets closest to your destination and is still running. You can see below for how to check on Naver Maps, but since you will be at the airport, you can also simply ask the staff for the best options.
If no route gets you exactly to the right place, you can transfer to a taxi afterwards, or of course it's always an option to take a taxi directly from the airport.
If you make the train, but arrive at Hongdae or Seoul station after midnight, you'll find out that the connecting subways are no longer running. To get to your final destination, it's usually best to take a taxi. This is the common way for people to get home after the subway has stopped running. To read more about taking taxis in Korea, continue here:
There are also night buses, but since they don't depart often it depends on the situation. Since taxis are affordable, it's usually the better option.
One final note is that Hongdae is a common nightlife area, so getting a taxi between 12AM-1AM (just after the subway has stopped service), can be a challenge. In this case it might be better to get off at a different station like Seoul station.
If you need to leave early in the morning, the first Airport Express train might not be early enough, or you might not be able to get to the Airport Express departing station because the subway isn't running yet. In this case, an airport bus is usually the best option. There are many routes, so it's likely that there is one departing near you.
Let's see how to check on Naver maps:
These buses are generally reliable and come on time. However, since it's understandably nerve-wracking to depend on one bus to make your flight, it might be worthwhile to read about taking taxis in Korea to have a back-up plan: