About 10% of the population is left-handed or non-right handed. Its brain organization and cognitive skills could differ in relation to right-handed subjects. Our current knowledge is far of get to know its etiology. The scientific literature is sufficiently wide as interesting to review its main contributions. The experimental studies undertake the last 30 years, but this current revision is centred on studies from the last 10 years. From them it is concluded that in Neuropsychology of the left-handedness there are great disagreements. The investigation needs to distinguish types of left-handedness or non-right-handedness, while it is not demonstrated that there is a single type of left-handedness.