Reading a few articles about podcasting in education reminded me of the term "Flipped Classroom." The concept of a flipped classroom is that students do the learning at home via the internet (watching videos or listening to podcasts), and then the homework in class where they can get help on assignments. I think this idea has some really great qualities. One aspect is that students can re-listen to the explanation of the topic without being worried about what the rest of the class thinks, or slowing down the rest of the class if they didn't get it the first time. I remember struggling with pre-calc in high school and a friend who went to a different school showed me a website that his pre-calc teacher had made with little video explanations and examples of specific math problems. It even had the answers, so I could make sure I was practicing correctly. I owe passing that class to those videos, which, at the time, were a novelty.
I think that podcasts definitely have a place in education, and as long as they don't get overused, they can be a great resource. Ideally, I would like to assign students to listen to podcasts for homework, but I don't feel that I can do that without isolating students without access to internet. I know that it's more uncommon than common these days to not have internet at home, but the school district I teach in has 70% free and reduced lunch students, including many refugees who don't have access to internet.