Dementia, a chronic and progressive cognitive declination of brain function due to disease or impairment, is becoming more prevalent due to the aging population. A major challenge in dementia is achieving the accurate and timely diagnosis. In recent years, neuroimaging with computer-aided algorithms have made remarkable advances in addressing this challenge. Much of the success of these approaches can be attributed to the application of machine learning and deep learning techniques for neuroimaging. In this review paper, we present a comprehensive survey of automated diagnostic approaches for dementia using medical image analysis and machine learning algorithms published in the previous five years (2013-2018). Based on the rigorous review of the existing works, we have found that while most of the studies focused on Alzheimer's disease have demonstrated reasonable performance, the identification of other types of dementia remains a major challenge. Hybrid imaging analysis through deep learning approaches may hold promises for early diagnosis of these other types of dementia, and warrant further investigation in the future. The main contributions of this review paper are as follows: 1. Based on the detailed analysis of the existing literature, this paper discusses the most recent neuroimaging procedures for dementia diagnosis, and 2. It systematically explains the machine learning techniques and, in particular, deep learning approaches for early detection of dementia.