What can be done about Clients who have not paid despite reminders?

What's the value in maintaining a relationship with a client that won't pay? Seems like they've already abandoned the relationship.

But if you've only been mailing them statements, you could try calling the person responsible for payables and talk to them. If that doesn't work, try calling the person who you contracted with initially and ask for their help directly.

It really depends on the sum of money and the circumstances. Have you worked with them before? If so, did they pay on time back then? Is it a small amount they owe you, or a large amount? Is your company dependent on this client to make ends meet? Do they have a department where invoices are handled, or is e.g. the CEO responsible for all the invoices? Try coming in contact with the right people, and immediately stop any current and future work you're doing for them until the invoice is paid. If you are able to, inform them you'll take offline the work that was not paid for in 4 weeks time (it's a drastic measure but you have sent them reminders multiple times already).

Like Steven said, what's the point of having client relations when they are not paying you? Their actions show they are not not invested in maintaining a relation with you

If you are in the UK, you can send a final demand stating that unless payment is received within (a reasonable time period), say 21 days, you will go to the small claims court.

https://www.gov.uk/make-court-claim-for-money