Podcasts are spoken documents across a wide-range of genres and styles, with growing listenership across the world, and a rapidly lowering barrier to entry for both listeners and creators. The great strides in search and recommendation in research and industry have yet to see impact in the podcast space, where recommendations are still largely driven by word of mouth. In this perspective paper, we highlight the many differences between podcasts and other media, and discuss our perspective on challenges and future research directions in the domain of podcast information access.