Recent years have seen increased interests in applying the latest technological innovations, including artificial intelligence (AI) and machine learning (ML), to the field of education. One of the main areas of interest to researchers is the use of ML to assist teachers in assessing students' work on the one hand and to promote effective self-tutoring on the other hand. In this paper, we present a survey of the latest ML approaches to the automated evaluation of students' natural language free-text, including both short answers to questions and full essays. Existing systematic literature reviews on the subject often emphasise an exhaustive and methodical study selection process and do not provide much detail on individual studies or a technical background to the task. In contrast, we present an accessible survey of the current state-of-the-art in student free-text evaluation and target a wider audience that is not necessarily familiar with the task or with ML-based text analysis in natural language processing (NLP). We motivate and contextualise the task from an application perspective, illustrate popular feature-based and neural model architectures and present a selection of the latest work in the area. We also remark on trends and challenges in the field.