The intermittent generation of non-dispatchable renewable distributed generation, along with the load variability, demand growth and electricity market prices impose operational uncertainties on the distribution network planning. The accurate and efficient modelling of these uncertainties is essential to guarantee the optimal integration of distributed energy resources in the distribution systems. This work firstly gives an overview of the generic distribution network planning and active distribution network planning. Then, the basic framework and the key features of the active distribution network planning are examined. Existing literature in the uncertainty modelling techniques is reviewed, discussed, and categorised into the following: probabilistic techniques, stochastic optimisation, robust optimisation, possibilistic techniques, hybrid probabilistic possibilistic techniques and information gap decision theory. The typical active distribution network planning problems include the distributed generation investment planning, optimal storage allocation, reliability assessment, probabilistic optimal power flow, optimal reactive power planning, substation expansion and feeder reconfiguration. A systematic summary and comparative evaluation of the uncertainty modelling techniques is provided, showing that there is no single best uncertainty modelling technique so far, and the choice of an appropriate technique depends upon the type of uncertain input variables and planning problem. This is followed by a discussion of additional challenges and their solutions in the context of active distribution network planning.