The convective drying of fruits is the most implemented drying technique to stabilize fruits and to increase their shelf life. The mathematical modelling of drying is a useful tool in process optimization and dryer design. The modelling involves the solution of complex partial differential equations of coupled heat, mass and momentum transfer, which can be solved by several numerical and analytical methods. The aim of this review is to present and analyse the main published researches on the modelling of the convective drying of fruits focused on theoretical models. The main parameters involved in the numerical modelling of fruit drying are presented, such as the main mathematical models in the conjugated or non conjugated approach, the applications on different geometries and dimensions, the scale approach, the thermophysical and transport properties determination, the alternatives of numerical solutions, the main methods to determine convective transfer coefficients, and other modelling considerations such as the shrinkage inclusion and quality deterioration are presented and analysed in this review based on the studies reported in the literature in the past decade. Through their comparison and analysis, future perspectives and challenges in fruit drying modelling are discussed. The computational tools increase the accuracy in predicted values and the possibility to extrapolate the characteristics from a micro-scale level to a macro-scale level. The challenges for convective drying of fruit lead to overcoming the dependence on empirical models for drying parameters determination, the lack of shrinkage inclusion and 3D modelling by means of advanced procedures such as multi-scale and conjugated modelling. The definition of the application of the model is important. Simple models present an effective use in some cases of engineering applications. More complex models are closer to reality and useful to engineering and research purposes. (C) 2017 Elsevier Ltd. All rights reserved.