I noticed that on my CentOS 6 box, I was still running nginx 1.0.15. I wanted to upgrade to nginx 1.10.1. However, when I ran sudo yum update nginx, it showed that there were no Packages marked for Update. Luckily, getting the latest version through Yum is straight-forward and only requires adding a new repo.

First, create a new file, nginx.repo, in the yum repo directory.

vim /etc/yum.repos.d/nginx.repo  

Next, give it the following contents:

[nginx] 
name=nginx repo  
baseurl=http://nginx.org/packages/centos/$releasever/$basearch/  
gpgcheck=0  
enabled=1  

Save the file, then shut down the nginx service (unnecessary if nginx wasn't on the system previously)

sudo service nginx stop  

Now, run the yum update command again (or install if nginx wasn't on the system previously)

sudo yum update nginx  

It should now let you update to the latest version! As soon as you install the new version, start nginx back up.

sudo service nginx start