The massive growth of mobile users and the essential need for high communication service quality necessitate the deployment of ultra-dense heterogeneous networks (HetNets) consisting of macro, micro, pico and femto cells. Each cell type provides different cell coverage and distinct system capacity in HetNets. This leads to the pressing need to balance loads between cells, especially with the random distribution of users in numerous mobility directions. This paper provides a survey on the intelligent load balancing models that have been developed in HetNets, including those based on the machine learning (ML) technology. The survey provides a guideline and a roadmap for developing cost-effective, flexible and intelligent load balancing models in future HetNets. An overview of the generic problem of load balancing is also presented. The concept of load balancing is first introduced, and its purpose, functionality and evaluation criteria are then explained. Besides, a basic load balancing model and its operational procedure are described. A comprehensive literature review is then conducted, including techniques and solutions of addressing the load balancing problem. The key performance indicators (KPIs) used in the evaluation of load balancing models in HetNets are presented, along with the concurrent optimisation of coverage (CCO) and mobility robustness optimisation (MRO) relationship of load balancing. A comprehensive literature review of ML-driven load balancing solutions is specifically accomplished to show the historical development of load balancing models. Finally, the current challenges in implementing these models are explained as well as the future operational aspects of load balancing.