Time travel stories rely on several "laws" or paradoxes, sometimes in conflict with one another:
the butterfly effect (as seen in Bradbury's A Sound of Thunder, the one about the dinosaur hunter stepping on a, literal, butterfly and coming back to a totalitarian future). This requires time travelers to be exceedingly careful and usually require lots of observation and fine-tuning (e.g. Asimov's Eternity).
the inertia effect (I remember Star Trek novel Ishmael) where small changes are actually absorbed and reversed by the time stream. For example, you go back to Sumer and kill a king. Back in the XXI century, all that it changes is that some symbols in a shard of pottery in a forgotten museum rearrange themselves. To have effect on the future, a change must be enormous enough to overcome Time's "inertia". This may mean that you can do almost anything in the past, provided it's sufficiently far back, with all the ethically sinister implications of that "anything".
the Grandfather Paradox. You go back in time and kill your own grandfather before he reproduces, or marry your mother and maybe even get her pregnant. Possibly then you change sex, go back again in time and are your own mother. How is this even possible? Solutions range from "it isn't", to the point that trying to build a time machine wrecks your civilisation or makes the Sun go supernova, to "it is and it isn't" (not completely resolved in David Weber's Apocalypse Troll) since every time you go back in time, you actually split the timestream in two, one where you did not appear (and is the one that gave birth to you) and one where you did (and had effect on the future). You can come back from a future where you can't exist because they are two completely separated futures. Both theories conflate in one story by... Greg Bear, possibly?, in which the timestream you left finds itself irredeemably short some 80 kg of mass, and the one you arrive in finds itself with an identical excess. Both continua are then doomed - in one the Sun goes out, in the other it balloons and ultimately goes nova.
The timeline split plus butterfly effect is the plot device at the basis of Eric Flint's 1632 (aka Ring of Fire) series, where a sizeable area of Earth's surface is swapped with a different area some four centuries earlier. The up-timers quickly conclude that they might as well do their best with what they have, and actually endeavour to change their would-be future as much as possible, rather than the reverse, since either they are in a parallel time-stream or they've already trashed that future just by being.