I often get asked this question and have helped a lot of businesses move from hosting provides to cloud providers like Amazon AWS, Microsoft Azure, Google Cloud Platform or Heroku and others. One of the advantages is that you manage or have visibility on the underlying technology hosting your site. Depending on the site you have you will need a virtual machine (old school), containers in Kubernetes or the best case will be to go serverless in the form of a Web App, Function or Lambda.