General kinetic models are established for the climb of edge and screw dislocations. The climb of a straight unconstrained edge dislocation is considered in terms of the diffusion of nonequilibrium point defects to (or from) the line and their absorption (emission) and destruction (creation) at the line. The climb is nucleated by the formation of short rows of defects which are attached to the edge of the extra plane and are bounded by jog pairs. Climb occurs by the growth of these aggregates until they destroy each other by mutual collisions. Noa prioriassumptions are made about the ability of either the dislocation or the jogs to maintain local point defect equilibrium during climb, and account is taken of rapid defect diffusion along the core. Effects of nonequilibrium defects in perturbing the jog population are also included. Equations describing this edge dislocation climb are developed but are left in a general form. Complete solutions are worked out in a following paper (Part II). Complications which arise when geometrical constraints and line curvature are present are discussed, and a description of the relationships between curvature, macroscopic line tension, and jog density is given. It is concluded that the results for the unconstrained climb model can be used in many such cases over a considerable range of conditions. The treatment of screw dislocation climb focuses attention on the climb of an initially straight dislocation into a multi‐turned helix. The detailed mechanisms are found to depend strongly upon the geometry and mobility of point defects and point defect aggregates on the core, and therefore only a qualitative theory is given. It is suggested that in many crystals vacancies largely dissociate into kinks when they enter the core, and that the helical turns build up rather uniformly along the line by the aggregation of ordered arrangements of these kinks.