Is there anything you should be looking out for in your data before fitting a Cox hazard model?

For example, with other kinds of models, like linear regression, you should check if your response is normally distributed. I'm wondering if it's the same for Cox proportional hazard models - if any variables need to follow a particular distribution or if there are any other important assumptions.

If so, what are common ways of finding and dealing with problems in this kind of data?

Thanks!