There has been an explosive growth in research over the last decade exploring machine learning techniques for analyzing chest X-ray (CXR) images for screening cardiopulmonary abnormalities. In particular, we have observed a strong interest in screening for tuberculosis (TB). This interest has coincided with the spectacular advances in deep learning (DL) that is primarily based on convolutional neural networks (CNNs). These advances have resulted in significant research contributions in DL techniques for TB screening using CXR images. We review the research studies published over the last five years (2016-2021). We identify data collections, methodical contributions, and highlight promising methods and challenges. Further, we discuss and compare studies and identify those that offer extension beyond binary decisions for TB, such as region-of-interest localization. In total, we systematically review 54 peer-reviewed research articles and perform meta-analysis.