The World Health Organization (WHO)’s list of neglected tropical diseases (NTDs) highlights conditions that are responsible for devastating health, social and economic consequences, and yet, they are overlooked and poorly resourced. The NTD list does not include conditions caused by Gram-negative bacilli (GNB). Infections due to GNB cause significant morbidity and mortality and are prevalent worldwide. Southeast Asia is a WHO region of low- and middle-income countries carrying the largest burden of NTDs. Two significant health threats in Southeast Asia are Burkholderia pseudomallei (causing melioidosis) and hypervirulent Klebsiella pneumoniae (HvKp). Both diseases have high mortality and increasing prevalence, yet both suffer from a lack of awareness, significant under-resourcing, incomplete epidemiological data, limited diagnostics, and a lack of evidence-based treatment. Emerging evidence shows that both melioidosis and HvKp are spreading globally, including in high-income countries, highlighting the potential future global threat they pose. In this article, we review both conditions, identifying current trends and challenges in Southeast Asia and areas for future research. We also argue that melioidosis and HvKp merit inclusion as NTDs, and that mandatory global surveillance and reporting systems should be established, and we make an urgent call for research to better understand, detect, and treat these neglected diseases.