-고 있어요 — is doing (right now)
지금 밥을 먹*고 있어요.* — I'm eating right now. Honorific: -고 계세요. Also for wearing: 안경을 쓰고 있어요 — he's wearing glasses.
-(으)려고 해요 — intend to, plan to
주말에 쉬*려고 해요.* — I'm planning to rest at the weekend. As a connector: 한국어를 배우*려고 책을 샀어요.* — I bought a book (in order) to learn Korean.
-(으)러 가다/오다 — go/come to (do)
Only with movement verbs: 밥 먹*으러 가요* — I'm going to eat. 놀*러 오세요!* — Come over (to hang out)!