SQLyog connects to MySQL using the native C-API from MySQL - the fastest and most effective way to manage MySQL. This API is compiled into SQLyog code itself.
Even if the TCP-port (3306) normally used by the MySQL server is blocked (as often is the case at ISP's) SQLyog still let you connect using HTTP(s)-tunneling or SSH-tunneling. And if you are behind a proxy SQLyog can handle that too.
The client for SSH connection is installed with SQLyog, and a PHP-script for HTTP-tunneling is too. That script must be uploaded to your webhost. The PHP-script uses php_mysql extension that is available practically everywhere where MySQL is available.
SQLyog works with MySQL version 3.23 and upwards.