The most important part of any travel event is, of course, having an itinerary and a ticket. An itinerary tells you where you are going to be and when and your ticket is your voucher (or authority and proof of payment) which lets you travel. Even in this technological day and age, each and every journey by air has a ticket. It may be electronic or even virtual, but a ticket there must be. The ticket, apart from being convincing proof that you have paid to travel, also tells you precisely what you have paid for and to whom.
As far as connections are concerned, the actual ticket, in all its glory, will tell you how your trip has been put together - and this is very important as HOW your trip is put together will dictate what responsibility any airline in your itinerary has with regard to any missed connections. Should you elect to cancel, then even on a non-refundable ticket, there are certain taxes which you would have paid, which you are still entitled to receive back - even if there is an administration fee involved. Unless you have a full copy of your ticket, you cannot tell what money you may be able to recover. I am always a little surprised that many air travelers are quite happy to hand over a significant amount of money, without establishing what they have paid for and to whom they have just given their money.
When you buy a ticket, you are not simply paying your airline. Take a ticket to the USA, from London, for example. You are paying a fare to the airline, you are paying the UK Government, you are paying the US Government (quite a lot, actually) you are paying the City authority of where you land, you are paying airports for your use of them and you are even paying something towards flora and fauna. Then you are paying some "carrier imposed surcharges" - which could be anything, really. A lot of those taxes paid to the various administrations, even with a non-refundable ticket, you are entitled to be repaid.
But I digress.
As far as this post is concerned, we need to look at how your ticket is put together. For flight connections to work, even though they may be shown as continuous on your itinerary, unless they are also continuous on your ticket - then they are not continuous. Unless you have sight of all of your ticket, then you will not be able to answer that question. There is a secondary back up to checking this.
So, for example, you are happy that you have your flight from LHR (London Heathrow) to JFK (New York) to BDL (Hartford, CT) all neatly written on one ticket. This means that if you flight arrives late into JFK, then you will be given a later connection if things go awry BUT if you have one ticket that shows, say, LHR to JFK and back to LHR and another ticket for the JFK to BDL part, the story is totally different. Your secondary check is to look at what is termed the "fare construction" - that is, how the fare is put together. A through ticket may have something like: LON (BA) X/JFK (AA) BDL M528.92
This reads as a British Airways flight from London to New York JFK and then on with an American Airlines flight to Hartford (the X/JFK means "no stopover"; a stopover being longer than 24 hours) and the M528.92 means the fare is calculated as being mileage and then the mileage figure charged. Airlines use something called "Neutral Units of Currency" which may then be converted at the prevailing rate into whatever currency you choose.
Given what I said in a previous post about Minimum Connecting Times and tickets, should your ticket's fare calculation look like the one mentioned above, then you can leave home in the certain knowledge that come what may, your airline will make sure that you get to your destination without any further fare or ticket costs. Do remember, however, what I said about EU and US (in this instance) regulations. Here, you would be leaving an EU airport so if you could not get a connecting flight until the next day, the delivering airline (in this example, British Airways) would need to make arrangements to look after you as well as arranging your onward journey.
As these factors are so important in making sure your travel works as seamlessly as it could do, it is, therefore, very important that you have sight of all of your ticket - best, in hard copy format. The ticket must have a ticket number. On any scheduled air ticket - any ticket - the first 3 digits of the number represent the airline issuing your ticket - 001 is American Airlines, 125 - British Airways, 932- Virgin Atlantic and so on; if someone has given you a "ticket" for scheduled (NOT charter - charter is different) and the ticket does not start with (3 digits of airline), then you do not have the ticket. So, a Virgin Atlantic ticket could be, say: 932 1074 289 603 (nearly all tickets follow the same 3-4-3-3 format).
The ticket will show the flights booked and paid for, the fare basis (vital for finding out what restrictions apply) the fare construction and a breakdown of what you have paid to whom by way of "taxes and charges". The ticket shows other bits as well, but the above are the most important. When sorting out previously-booked-online travel disasters, then the first thing any agent would need to know is what your actual ticket is telling us. We may not be able to fix it (If we didn't book it, we can't fix it so - go see your travel agent first!) but at least, we can point you in the right direction.
In fine, despite the trend for having everything to hand on your smartphone, there is a real need to make sure you have got a hard copy of your ticket and your itinerary as well - but mainly, your ticket. Too many people - far too many people - are prepared to travel, assuming that "tech" has done its bit. Fine, if all goes well, but as soon as things start to go pear-shaped, then having hard copy of these two items will make things a whole lot easier.