The use of psychic powers is encompassed by the term psionics. Individual creatures capable of employing such powers are described as psychic or psykers. There are, of course, countless other names applied to these creatures (some rather derisory). Within human society they might be called witches, warlocks, telepaths or any one of countless other names.
Psionics are very simple in Rogue Trader. Each psyker has a psionic level (Mastery 1-4) and a number of psychic points or psi-points related to that level (10 points per level or 3D6 per level if you prefer random generation). To employ an ability, a psyker simply pays the appropriate number of psychic points. Low level abilities may only cost 1 or 2 points while level four powers might coast as many as 12 points to cast. Psykers have a limited number of powers they can choose from, typically 3 or 1D6 per level of mastery.
As long as a psyker has 12 or more psi-points the power may be used without testing for success. If the psyker has less than 12 points, he must test to see if his powers work. Roll 2D6... if the result is less than or equal to the psyker's remaining psi-points, the power is cast. If the roll fails, so does the power. Note that the psi-points used to attempt the use of the power are lost whether it works or not.
The target of the attack may attempt to make a saving throw. Each model affected rolls 2D6 - if the roll is equal to or less than the target's Willpower, the power has no effect. A psyker may use additional psi-points to force a penalty on this save (-1 per additional psi-point spent), but must declare the intention to do so before the saving throw is rolled. A psyker may also expend psi-points to augment his own save against psionic attack in the same manner.
There are 40 psychic powers available in the game (10 of each level). I'm not going to list them all, but it's worth noting there are abilities besides attack spells that allow psykers to employ telepathy, teleport, affect psychology, or improve their defenses.
There are more than five pages in Rogue Trader dedicated to mutations, suggesting it was initially intended to be a larger part in the game than we see today - and this was before Chaos was a recognized antagonist in the game. Even families with no past history of mutation might expect to run a 5% risk of mutated offspring, while the chance among mutant parents is 90%.
The position of Mutants within the Imperium varies from world to world. On the majority of primitive and medieval worlds they are slain as soon as they are born. On the majority of technically advanced worlds they are permitted to live, but rarely enjoy the boon of full citizenship. On many worlds they are segregated from the normal population, outlawed, or forbidden to live in certain areas. Generally speaking, they form a huge downtrodden portion of the population of the Imperium. Their dissatisfaction occasionally erupts as rebellion. Such revolts occasionally allow mutants to take control of planets or even groups of planets for a short period. Usually, however, retaliation is swift and effective.
A mutant may be created by staring with any basic profile and adding D3 mutations. There are almost a hundred mutations provided (as well as a fun random table), ranging from purely cosmetic to abilities that improve ability characteristics, provide unusual attacks or means of movement, or even hinder the mutant in some manner. In general, these abilities seem less powerful than the ones presented in the Realm of Chaos books that follow.