Chemex has a devoted following of folks ...count my own mother as one of them. Invented by a chemist to improve filter brewing, the cornerstone of this method is Chemex’s branded filter; they are 20-30% heavier than any other filter and have a special paper formulation to remove sediment but allow positive aromatic compounds to pass through The fine paper grain holds back "mud," while permitting correct filtration speed. Chemex brews at least 1-2 minutes slower than normal paper filters, more in line with the optimal time that hot water and grinds should contact each other: 4 minutes. The Chemex filter paper is heavy and can impart a paper taste, so pre-rinsing is essential.
The Chemex brewer is all glass, which makes it very easy to clean. Maybe the best thing about the Chemex is that you can see the process, interact, and make changes. There's a lot to be said for that and we shouldn't dismiss it.
Everyone has their own pouring technique (let the coffee pre-infuse/bloom or not, pre-wet the filter, pour at a particular rate) and the results are there in the cup. Machines don't typically allow for this.
Want to impress your friends? Tell them that your Chemex is in the permanent collection of the Museum of Modern Art in New York. We have a page with full instructions for Chemex brewing.