The object of the research is the line segmentation task. To recognize the handwritten text from the documents in image format offline handwriting recognition technology is used. The text recognizer module accepts input as separate lines, so one of the important preprocessing steps is the detection and splitting of all handwritten text into distinct lines. In this paper, the handwritten text line segmentation task, its requirements, problems, and challenges are examined. Two main approaches for this task that are used in modern recognition systems are reviewed. These approaches are statistical projection-based methods and neural-based methods. Multiple works and research papers for each type of approach are reviewed analyzing their strengths and weaknesses considering the described tasks, constraints, and input data peculiarities. Overall acquired results are formed in a single table for comparison. Based on the latest works that utilize deep neural networks the new possibilities of using these methods in recognition systems are described that were unavailable with traditional statistical segmentation approaches. The constructive conclusions are made based on the review, describing the main pros and cons of these two approaches for the line segmentation task. These results can be further used for the correct selection of suitable methods in handwriting recognition systems to improve their performance and quality, and for further research in this area.