As of now current nginx version in centos 7 repo is 1.12.2, but latest version of stable nginx is 1.14.1.

In this article we will install latest nginx/1.14.1 in Centos 7.

1. Remove current version of nginx (1.12.2)

sudo yum remove nginx*

1.1 (optional) You can also move nginx configuration folder into different one, so that your installation will be clean, without any old configs. Then you just need to enable your sites again, one by one.

sudo mv /etc/nginx/ /etc/nginx.bak

2. Disable nginx from centos repo:

# open this file
sudo vi /etc/yum.repos.d/epel.repo

# and append one line to [epel] section:
[epel]
...
exclude=nginx*

3. Create file /etc/yum.repos.d/nginx.repo:

sudo vi /etc/yum.repos.d/nginx.repo

with the following content:

[nginx]
name=nginx repo
baseurl=http://nginx.org/packages/centos/7/$basearch/
gpgcheck=0
enabled=1

4. Update

sudo yum update

5. Install nginx (1.14.1)

sudo yum install nginx

6. Enable nginx service and start it

sudo systemctl enable nginx
sudo systemctl start nginx

7. Check nginx status:

sudo systemctl status nginx

You should see something like this:

● nginx.service - nginx - high performance web server
   Loaded: loaded (/usr/lib/systemd/system/nginx.service; disabled; vendor preset: disabled)
   Active: active (running) since Wed 2018-11-07 07:28:58 UTC; 6s ago
     Docs: http://nginx.org/en/docs/
  Process: 31152 ExecStart=/usr/sbin/nginx -c /etc/nginx/nginx.conf (code=exited, status=0/SUCCESS)
 Main PID: 31153 (nginx)
   CGroup: /system.slice/nginx.service
           ├─31153 nginx: master process /usr/sbin/nginx -c /etc/nginx/nginx.conf
           └─31154 nginx: worker process

It means that nginx is installed successfully.

P.S. If you're using fastcgi in nginx, please also check this article.