Ecosystems and the communities they support are changing at alarmingly rapid rates. Tracking species diversity is vital to managing these stressed habitats. Yet, quantifying and monitoring biodiversity is often challenging, especially in ocean habitats. Given that many animals make sounds, these cues travel efficiently under water, and emerging technologies are increasingly cost-effective, passive acoustics (a long-standing ocean observation method) is now a potential means of quantifying and monitoring marine biodiversity. Properly applying acoustics for biodiversity assessments is vital. Our goal here is to provide a timely consideration of emerging methods using passive acoustics to measure marine biodiversity. We provide a summary of the brief history of using passive acoustics to assess marine biodiversity and community structure, a critical assessment of the challenges faced, and outline recommended practices and considerations for acoustic biodiversity measurements. We focused on temperate and tropical seas, where much of the acoustic biodiversity work has been conducted. Overall, we suggest a cautious approach to applying current acoustic indices to assess marine biodiversity. Key needs are preliminary data and sampling sufficiently to capture the patterns and variability of a habitat. Yet with new analytical tools including source separation and supervised machine learning, there is substantial promise in marine acoustic diversity assessment methods.