Here are some of the best readings about shmups available on the Internet.
If you're new to the genre I recommend reading the first ones before venturing into the others.
One Credit Completion
A very good introductory text on the nature and the importance of the
1CC for all kinds of video games (not only shmups), by Mike Molinari.
A Beginner's Guide to 2D Shooters
Bulletmagnet covers everything you need to know about shmups with great insight. History, conventions, subgenres, scoring, developers, home systems, gameplay hints and a lot more.
Understanding Scrolling Shooters
Catstronaut discusses the nature of shmups and the fascinating meanderings of the genre, examples given.
Games that defined the Shmup genre
Shmup staples and the most famous shmup franchises are highlighted by Bulletmagnet in this excellent article.
An essay on shmup bosses and their quirks and perks, by Mike Molinari.
Why are shmups so unpopular
An article at Continue that takes a quick look at the prejudice caused to the genre by mainstream reviewers.
Arcade Culture (unavailable - if you find it again please drop a comment below)
Polarizing and polemic Alex "icycalm" Kierkegaard writes about Japanese arcade culture and the reasons for the existing chasm between East and West with regards to credit feeding.
The Full Extent of the Jam (PDF)
Expert French shmupper Prometheus offers a comprehensive guide on how to approach bullet hell and consistently improve your skills, using as example everybody's favorite Cave classic DoDonPachi.
Real Men Play Gradius
Aaron Linde delivers a very inspiring text about the concept of being hardcore and its elusive connections to the shmup genre.
The Pablum Era
The word "shmup" isn't mentioned a single time in this text by Scott C. Jones, but the content reverberates deeply within this often neglected branch of video games.
Shmups - Forgotten Essentials
Bulletmagnet discusses gameplay aspects that many people take for granted when playing, reviewing or designing shmups.
Don't know what those nerds are talking about? Well, this is the place to go for answers! Admin by Bulletmagnet.