Time travel is a popular notion in science fiction and has been verified by measurement to be fully possible with fairly well defined limitations and interpretations. The simplest example is current time as it continually moves forward along with everything in it. This moving forward in time is generally not considered real time travel as it is the normal configuration and so really only going forward much faster in time or even backwards in time is generally considered to be the popular notion of time travel.
Special relativity has been confirmed in a large number of experimental and empirical observations to demonstrate that moving clocks really do run slow. This can be taken to the extreme that an astronaut on a rocket ship moving near the speed of light would appear to be almost frozen in time. From all the physical indications you could make on the astronaut or rocket, you would have to conclude that time is moving slower on the rocket than it is compared to you. Does this mean that the astronaut is traveling backwards in time relative to you as the clock on the rocket is lagging behind yours? It is true that the astronauts clock would be ticking more slowly than yours from your perspective but the evidence also shows that the astronaut on the rocket would say the same about you. The astronaut would have to also conclude that your time is moving extremely slow, almost frozen in time relative to that of the rocket. So the astronaut sees the clock on the rocket just ticking along fine while yours appears to be ticking slow. The real reason for this apparent paradox is that the speed of light is the same value in both reference frames, the astronaut and you can be shining flashlights in any direction and both of you will see the light rays from each traveling at the speed of light. The wavelength of the light will change so that the flashlights color will depend on the relative motion but the concept of simultaneous events has to carefully be evaluated to understand this effect.
Another form of empirically verified time dependency in what we consider normal time evolution comes from general relativity which shows that time moves more slowly in gravitational fields. The stronger the gravitational field, the slower a clock will tick. A black hole in principle can stop time at a certain distance from its center known as the event horizon (where events effectively stop occurring). This is actually an effect which has to be corrected for in global positioning system (GPS) measurements as the time evolution on satellites is not the same as those on earth due to this effect. So to a very small degree, you would age faster in space than here on earth.
Travel backwards in time is mathematically consistent with all known physical phenomenon but not in the way you probably expect, there are some caveats. The existence of antimatter has been empirically known for almost 100 years now. The antiparticle for an electron can either be called an anti-electron or a positron. A normal electron has a negative charge and an anti-electron has a positive charge. Similarly a proton has a positive charge but an anti-proton has a negative charge. Whenever a normal particle comes into contact with its antiparticle, they annihilate each other and are converted into pure energy in the form of gamma ray photons. All anti-matter particles are effectively equivalent to their normal matter counterparts with the exception that anti-matter can be considered to have negative energy. The difference in energy when an anti-matter particle encounters its matter counterpart is simply total energy of the gamma rays released when they annihilate each other.
Equivalently it can be said that other than the charge on particles of antimatter, they are identical in every respect to their normal matter counterparts. In terms of the known laws of physics, antimatter behaves mathematically equivalent to normal matter simply traveling backwards in time. Effectively antimatter particles are indistinguishable from normal matter traveling backwards in time on a particle by particle basis. The second law of thermodynamics would effectively limit any large scale effects of reverse time travel for antimatter though. This is to say that a swing may appear the same if it were on a movie going back and forth even if the movie were going backwards until you saw its height slowly growing over time. Spilling water, mixing separate liquids or an explosion all show the second law of thermodynamics forcing randomness and disorder to always increase in any closed system with passing time which can then always be used to determine the true direction of time in any process.
Even without that, making antimatter is extremely difficult, the most complicated anti-matter material we can construct today is an anti-hydrogen atom. Creating just one single molecule of anti-water is way, way out of our reach as the energy required to make that single anti-oxygen atom is many orders of magnitude larger than our strongest accelerators in existence today. Being unable to make anti-water is indicative of how much more difficult it would be to make a single anti-sugar molecule or anything more sophisticated.
Time travel effectively occurs all the time in nature and in many ways but the Hollywood versions are largely pure science fiction.