The term ex usually brings a strong sense of finality to it. It's a harsh term, and it's hard to use it without thinking of a firm transition from one state to another. However, anyone pining for a significant other of the past should give that fact a little extra thought. The very nature of how we frame relationships in our mind will often be the driving force within it. Of course a relationship is over when both people agree on that fact and put a label on it. But sometimes those feelings just don't go away. The first step in bringing back an old flame is remembering that the term ex is just a simple label. Stop thinking of that person as an ex. Think of them instead in a more positive way.
If you have a hunch that they still have some feelings for you than it's best to frame it as a relationship that's simply on pause. And in that case it's up to you to hit play once again on the relationship. Sadly, there's not really a one size fits all solution to the problem. The most important aspect of this step is to tackle something that's often the main reason relationships fail in the first place. People need to really understand and pay attention to their former partner's individuality. A lot of times people get too caught up in the idea that men like certain things, and women like other things. Some of it might be valid. But the reality is that you're not interested in the totality or average of a gender. You're interested in one specific and unique person within it. And to get them back it's vital to really understand them as a person. And while that in general is important, there's one portion of it which is especially significant. You'll need to understand their current emotional and intellectual relation to you.
It's an easy mistake to simply wonder what they think of you. But that discounts how relationships work, and how they fail. People don't relate to romantic partners in the same way that they do to, say, their accountant. Objectivity doesn't factor in as fully when it comes to romance. At the same time, it's not all about emotion either. A relationship is something like a bridge which sits soundly in the middle of both factors. You can come up with a list of every trait you look for in a partner and on encountering them in real life there simply might not be a spark. At the same time, when that spark is there with someone that doesn't offer what you need than it won't work either. This is why you need to look at how a former romantic partner relates to you on both levels.
The most common situation will involve a partner who still has an emotional connection but who has lost the intellectual. He or she will still feel that you're a romantic possibility, but they're intellectually opposed to it. This is why people so often dial an ex after a night on the town. When they stop telling themselves that it's over the emotion can rise again. Of course in the real world one needs a more permanent solution to the problem.
Again, this is something which will vary on a person by person basis. But there's usually two possible roads to take which will bring them back to you. Both operate on the idea that you need to let their emotions build to the point where their intellect can evaluate things in a new light. You need to give them a moment to pause and realize that they're hurting themselves by not coming back to you.
Both solutions also operate on proximity. Depending on how they relate to you, and to dating in general, you'll need to either remove yourself from their social life for a while or fully integrate yourself into it. Again, the point here is that you're going to allow their emotional connection to you to explode in love.
If they need you in their life as a friend after the relationship is over than it's sometimes best to remove yourself from that situation for a while. Simply say that you still have feelings for them and that just being friends is too painful at the moment. Make it clear that you don't know how long you need to be away from them. In these cases the former partner is in a situation where they were still getting some of the good parts of the relationship without being in the relationship. When that's removed they'll often come running back and want to give the relationship another chance.
In other cases, you might need to further integrate yourself in the life of your ex. This is a chance to continually demonstrate that you've grown past any issues they had, and to remind them how great you are. While it might seem petty, you should also not be afraid to play on any issues with their new relationships. Don't be so obvious as to say anything. But if the new partner is failing in some area, make sure you're excelling in it. Then at some point confess that you still have feelings for them. This will allow a new and improved version of you to grow in their mind to match any lingering emotion. If all of these aspects of a relationship are kept in mind than it really is possible to get an ex back.