The phone call test
If someone calls and says ¿Vienes?, they're asking whether you're coming to where THEY are. You would respond Sí, ya voy (Yes, I'm on my way) — using ir, because from your position you're moving away toward them.
Ir + a + infinitive: the near future
The construction ir + a + infinitive is the most common way to express the near future in conversational Spanish — far more common than the formal future tense: Voy a llamarte (I'm going to call you). This construction uses ir, never venir.
Venir + gerund
Like llevar, venir can be combined with a gerund to express an ongoing action: Viene diciéndolo desde hace años (He's been saying it for years).