SummaryThe study of crossing‐over leads us on the one hand to consideration of the physio‐chemical nature and behaviour of the chromosomes, and, on the other to conclusions respecting the better‐known phenomena of segregation, pairing, recombination and gene action. Although many aspects of the cause and consequence of crossing–over are still not fully analysed, important conclusions have already been reached.The chiasmatype theory, that crossing–over is the sole condition of chiasma formation, allows of the accurate co‐ordination of the genetical and cytological methods of study of crossing–over. The genetical method consists of marking alternative chromosomes by the use of gene allelomorphs, the segregation and recombination of which may be followed. The cytological method is that of direct observation. The two methods are complementary in their natures.Crossing–over occurs when the pachytene chromosomes divide and tends to occur in definite positions in the chromosome, as a result of a special time and spacial sequence in formation. The positions are related to fixed points, viz. the centromeres and, possibly, the ends of the chromosomes.The movements of the chromosomes in crossing–over are related to coiling although the generation and distribution of the energy are not fully understood. Pachytene pairing is directionally specific, i.e. the chromomeres or pairing units are asymmetrical in type. The chromosomes show definite longitudinal cohesion and can transmit stresses along their length. Splitting of the chromosomes generates or releases such stresses, which may be transmitted and partially accommodated in unsplit regions. The unaccommodated stresses result in crossing–over.The frequency of recombination of loci is related algebraically to the frequency of crossing–over between them by the alternate terms of a binomial expansion. The relation may be expressed empirically in a logarithmic form. In the absence of chromatid interference recombination cannot exceed 50 per cent. Chromatid interference may result in a slight increase of this level.The frequency of reductional and equational separation of a locus depends on the behaviour at the centromere and on the frequency of crossing–over between the locus and the centromere. The relation is of the form of a summed geometrical series. Segregation in aberrant diploid and in autopolyploid types depends on the frequency of these types of separation. Although the limiting value of recombination may be reached when the loci concerned are but little more than 50 map units apart, they may still show correlated separation.Metaphase pairing and anaphase disjunction of the meiotic chromosomes is dependent, in the vast majority of cases, on chiasma formation. The regular occurrence of crossing–over is almost universally necessary for full fertility. In cases where the sexes differ in the manner of meiotic pairing, notably Drosophila, there is a corresponding variation in segregation, recombination, and disjunction.The presumably widespread occurrence of primary structural change, mainly duplication and inversion, leads to the regular occurrence of variant types by crossing–over. These, as in Oenothera and Drosophila, often have distinctive physiological characteristics and so are a source of material for the action of natural selection.The frequency of crossing–over per bivalent is open to selective action, and probably reaches an optimum value in any organism. This will chiefly result from its effects on the recombination of advantageous mutants.