Cross-lingual dependency parsing approaches have been employed to develop dependency parsers for the languages for which little or no treebanks are available using the treebanks of other languages. A language for which the cross-lingual parser is developed is usually referred to as the target language and the language whose treebank is used to train the cross-lingual parser model is referred to as the source language. The cross-lingual parsing approaches for dependency parsing may be broadly classified into three categories: model transfer, annotation projection, and treebank translation. This survey provides an overview of the various aspects of the model transfer approach of cross-lingual dependency parsing. In this survey, we present a classification of the model transfer approaches based on the different aspects of the method. We discuss some of the challenges associated with cross-lingual parsing and the techniques used to address these challenges. In order to address the difference in vocabulary between two languages, some approaches use only non-lexical features of the words to train the models while others use shared representations of the words. Some approaches address the morphological differences by chunk-level transfer rather than word-level transfer. The syntactic differences between the source and target languages are sometimes addressed by transforming the source language treebanks or by combining the resources of multiple source languages. Besides cross-lingual transfer parser models may be developed for a specific target language or it may be trained to parse sentences of multiple languages. With respect to the above-mentioned aspects, we look at the different ways in which the methods can be classified. We further classify and discuss the different approaches from the perspective of the corresponding aspects. We also demonstrate the performance of the transferred models under different settings corresponding to the classification aspects on a common dataset.