In this section I won't describe the behavior of all livebearers, for that will be noted in the section of all specific livebearer species sections.
In this section the focus is more to give an impression of the behavior in general.

The behavior of all the different livebearer species can not be compared to eachother There are friendly livebearers and semi-aggressive and aggressive livebearers. But even amongst friendly livebearers, aggression can be at hand.  It could mean that they are defending their territory, or it could be a matter of mating choice but aggression can also occur when a pecking order is developing in a group which makes it clear that it's a dominance thing. And be aware of it, that this dominance can happen to both male and female. So, the gender itself is not a reference in becoming dominant.

The eternal question that is going on when it comes to livebearers... Are they rabbits in water? A metaphor for the prolific nature of livebearers. Well, "yes" and "no", would be the answer... For it depends on the kind of livebearer. Most people only know the most common and commercial livebearer species and relate the level of reproduction to those. But in reality, there's a serious number of livebearer species that aren't that prolific. This means that the gestation period can take longer, or the number of newborns is low or even that they're hard to breed. This last thing mentioned, could mean that they need specific facilities in order to be able to be reproductive.

Do all livebearers have a courtship? "No", would be the answer to this question. Not all male livebearers will wear down a female to get a chance to mate with her. If we look at ovoviviparous livebearers, the males will have a gonopodium. But the size of the gonopodium is crucial in order to know wether a specific livebearer species will have a courtship or not.  Ovoviviparous livebearers where the males have a long gonopodium and a smooth tip won't have a courtship. For such males can direct their gonopodium directly to the female's vent. Males of ovoviviparous livebearers which have a shorter gonopodium, will have a courtship. For those males need to do more their best to get close to the female's vent. And such males do have another aid. And that is the fact that at the tip of their gonopodium, they have a number of hooks (the number of hooks depends on the kind of livebearer). These hooks makes it possible once they have directed their gonopodium to the female's vent, to make a connection  in order to donate their sperm packets at the opening of the female's vent. So, the gonopodium itself does not enter the female's vent. It only makes a short connection (split second).

Viviparous livebearers do have a courtship. For also males of viviparous livebearers need the time to get as close as possible with their andropodium to the female's vent.

The courtship of both ovoviviparous and viviparous livebearers can consists of a dance  of the male by circling around the female. The chasing itself has got nothing to do with the courtship. Note that the female itself decides wether she gives in to a male to mate with her or not. Even though a male can chase a female all day long and direct his gonopodium in her direction, as long as she won't give in, no actual mating will take place. The only exception there is, is that a very young naive female doesn't know that she's in charge.

Do adult livebearers eat their newborns? "Yes" and "no"...  It depends firstly on the kind of livebearer we're dealing with. Yes, there are enthusiast fry eaters. But there are also a reasonable number of livebearer species that won't chase nor eat their fry. A big part of the goodeid species won't chase nor eat their fry. But that has got also to do with the size of the newborns. Many goodeid species have large offspring at birth in comparison to the size of the mother. Halfbeaks however are tricky. Most large sized halfbeak species will leave their fry alone. But smaller sized adult halfbeaks tend to chase their young faster. But those newborns are also smaller.

But the general thing we know about adult fish eating their young has got also to do that they haven't been accustomed to smaller fish around them. What I know from experience is that if you give it a chance to let other fish get used to smaller tankmates, the chase on  fry will get less . Sometimes, the whole chasing even stops... But most people don't have the patience to let those big ones get used to such small ones.  My own experience is also when I purchase a new group of livebearers, I'd choose to purchase different sizes of that species. That really helps to avoid fry chasing and fry eating.

Below: An adult berliner swordtail (in the USA they call these swordtails "green lantern swordtails"). But the official name is "berliner swordtail". This female was dropping fry and at the end she had a batch of 74 fry. None were eaten by the mother. She stayed in this tank with the fry for 48 hours after birth.

Do pregnant females which are almost due, wander off or hide? Well again, yes and no. This depends on the kind of livebearer.There are females that seperate themselves from the group, there are females that start to hide more and there are females that just drop those fry during swimming as if nothing happens... Female guppies however are not very predictable. For each individual female guppy choses one of the mentioned methods.

Are breeder boxes really that bad? The answer is "no". But I'm not a very big fan of it either. But that's just personal. Nowadays, a lot of people resent using such a breeder box. For according to them it would be too stressful. Back in the 1960's, 1970's and 1980's we all used them without any problems. No one would've complaint about it back in the days. But I do get it why people resent them. If you'd put a pregnant female which is almost due in such a breeder box, it would be more stressful to be in a very small environment while she's used to much more space. But the fact that she's almost due triggers already a certain kind of stress itself. So, a smaller environment is adding more stress in this case. That will stress her out. But a female that has got still a week or two ahead before delivering, can be put in a breeder box without any problems. For she hasn't the stress level yet that an almost due one has. It didn't stress nor hurt the females back in time, so why would it be any  different nowadays?
The story about dropping undeveloped eggs or embryos  because of stress is nonsense. It's a story that was kept high for many years just to give an explanation why they were undeveloped. The correct story is that those undeveloped embryos or eggs would've never become fully developed embryos from the start. It's got to do with the amount of nutrients in the yolk sac. Usually, every egg has been pre-fertilized by the mother herself. Pre-fertilization means, that the mother provides the eggs of nutrients before any fertlilization has taken place. So that the developing embryos can feed themselves on those nutrients during the gestation period. If there's a lack of nutrients in a yolk sac, the eggs and/or embryo will not fully develop. When a female gets stressed, she will drop those undeveloped ones first. Simply because those are easier to release. So, the undeveloped eggs /embryos have got nothing to do with stress. 

Below: An undeveloped embryo. The eyes are already visible.

Light intensity can be of influence on the intensity of male coloration in multiple livebearers such as guppies for instance. If we don't look at predation but only to the amount of light available, the more light or the more intense the available light may be, underlaying colors in male guppies will be more exposed than when less light or less intense light is available. This results is more attention of the female guppies towards the more colorful males. The males will show a more brighter courtship than usual. 

If we take predation to the scene, the courtship of the livebearers will be during sundown and sunrise. This is because the male livebearers can see enough to court and the females are still able to see the color brightness of those males but will be less visible to predators.

Another aspect of daylight influence is that the more daylight available, the more larger the fish becomes. When kept with less daylight, the general result will be smaller adult specimens. 

Glass surfing

Not just livebearers but also other fish can glass surf. It means that a fish will go up and down or go from left to right in front of the glass. Usually, it means that a fish doesn't feel comfortable enough in the tank. A water parameter check would be in play to solve this problem. But it can also mean that a fish is trying to impress its own reflection. In such a case, there's nothing to be worried about. Just like this swordtail male shown below. He's flaring his fins while going up and down to impress his reflection.