I was recently looking for a ticket and one of the cheapest options included a stop-over for only 30 minutes at a major international airport. I estimated it would be impossible to catch the connecting flight and bought a different ticket. Later I wondered: what would happen if I bought a ticket with such a tight connection that it would make it almost impossible to catch the connection? Would the airline be responsible to get you on the next flight? Would you receive compensation? Who would determine whether you should have made it in time but you didn’t? Is there a general international legislation or is it left to the policy of each different airline?
Generally an airline is responsible for your connection between flights issued on a single ticket. Airports have a minimum connection time which limits how short a connection is allowed when ticketing. That time sometimes depends on factors like terminal changes but is in my opinion highly optimistic.
When you buy from a third-party agent you are not always issued a single ticket and if that is the case you are generally on your own but if it is the same airline, they sometimes take care of your missed connection. In most cases through major online travel agencies, they show mostly single ticket fares with those that are not labelled differently. Last time I saw such an offer, it said Hacker Fare below the price.
When you miss a connection for which the airline is responsible, they usually book you on their next available flight. This may set you back a few hours but a whole is not uncommon as certain segments only have daily flights. During high-season, they vary their strategy in include partner airlines and/or more complicated flights. This can be particularly grueling when all flights are booked for days and they put you on each waiting list in hopes that someone will cancel or miss their connection. Same if you were going to miss another connecting flight and they try to make you catch up to your next connection or go through an entire different route.
As for compensation, that varies considerably by jurisdiction. It ranges from nothing at all to hotel and monetary compensation. Better ask another question if you have a region or airline in mind.
Note: Generally means that there are exceptions with areas, countries, unions and airlines having their own rules and interpretation of the law can vary. Finally, even if you have the legal right to something, that does not mean that it will be given to you automatically.
When you buy a ticket from an airline they are on the hook for getting to your destination. So they will not sell tickets with impossible connections. Every airport has a minimum connection time, and for some airports that can indeed be as low as 30 minutes.
In Europe competition between airlines is fierce. And for example when Lufthansa offers a ZRH-MUC-HEL ticket this is in competition with Finnair's direct flights, so they will want to offer as short a connection as possible.
For this reason European Hub airports are often setup to make such short connections possible.
When connecting there are several scenarios. In those countries of Europe that are part of the Schengen agreement flights are divided in "internal" to Schengen, and "external". You can compare that to "domestic" and "international" in the US. For external flights another important distinction is that between "clean" origins, which have the same security standards as the EU (eg. USA, CA), and "non clean".
All Schengen airports are considered "clean". So most airports nowadays do not separate arriving and departing Schengen passengers. When you get of the plane you get discharged directly in to the Schengen departure concourse, where you just walk to your next gate. Minimum transfer time than just becomes the time one would need to walk between the gate pair that is furthest apart, and can easily be as low as 20 min.
For non-Schengen to non-Schengen it depends if you arrive "clean" or not. If you arrive "clean" many airports will also directly send you to the non-Schengen departure concourse. So short connections are easy there as well. If you connect to a Schengen destination you will need to go through passport control which can be fast too.
If you arrive from a "non clean" destination you will need to pass through security. Often passengers with short connection get access to the fast track lane.
Some airports are setup for very fast connections. Munich (MUC) is an example. Frankfurt is an example where fast connections are still possible if you do not think to much and just follow the signs.
Last week I travelled EDI to ZRH via FRA. The connection as scheduled was going to be just one hour. My plane from EDI however left half an hour late. We were parked at a remote stand (about as far away as possible it seemed) and bussed in. And for some reason we got bussed to a "non clean, non Schengen" gate in stead of a "clean, non Schengen" gate. I got there as my next flight had already been boarding for 10 minutes. I had to go through security (took 7 minutes) and passport control (took 10 seconds) and arrived at my next flight just in time to still be allowed on board. Had I missed it then LH would have just put me on the next ZRH bound flight. (There were for more departures to ZRH that evening.)
It is actually remarkable how long a minute really is...