In CentOS 7 MySQL has been officially deprecated and the database of choice is MariaDB

What's MariaDB?

MariaDB is a fork of MySQL created by the lead developers of MySQL when Oracle acquired Sun.
A detailed history about MariaDB can be found here
As far as feature comparison there is a good article on MariaDB show casing the technical differences.

Installing MySQL

First, add the community MySQL repo to CentOS:

rpm -Uvh http://dev.mysql.com/get/mysql-community-release-el7-5.noarch.rpm  

Second, install MySQL:

yum install -y mysql-server  

Finally, enable start on boot

chkconfig mysqld on