To do both vascular (angio, stent +/- graft, embolization, access) and non-vascular (biopsy, biliary, drainage, GU, GI and more) body intervention, you need to do a 5 year radiology residency + 1 year IR or the six-year integrated IR track (fast-track radiology residency with more time in IR and related clinical services like vascular sx).
You can also train in vascular intervention as a vascular surgeon (5 years GS + 2 year vascular fellowship (may include angio) +/- 1 year angio fellowship.
To do Neuro/head/neck intervention (INR), you generally need to do radiology + 1(or2) years diagnostic neuroradiology + 1-2 years interventional. Some body IR guys are also training in INR (add 6mo - 1 yr fellowship.) As well, neurosurgeons can train in INR (typically after or during a vascular NSX fellowship--> 6 years +1-2 +?????)...
Finally, I should add that you can do some peripheral interventions after certain interv. cardiology fellowships, but they are mainly focussing on a couple lucrative but repetitive procedures (carotid, renal, stent, stent, stent).
And note that some non-vascular intervention is also performed by related surgeons (i.e breast biopsy, nephrostomy, etc).
Radiology is the only route to the "whole spectrum" of what is called interventional radiology, but unsurprisingly, the lines are blurred as IR interfaces with many procedural specialties.