Know of Workflow software (as a modern web service)?

Hi everyone, question. I'm looking for a workflow system to help manage a team. Our work is very process driven: when person X finishes with this, give it to person Y. Person Y then confirms this, then sends it to person Z. When person Z finishes it, then... and so forth. All the systems I can find to do this feel like they're 30 years, does anyone know of a Ycombinator-style company or site that helps solve this? Note: I would pay non-trivial money to subscribe to a service that did this. Thanks! morgan