日語 Japanese Ask Questions Thread2 質問

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Japanese - Ask questions thread
http://dis.4chan.org/read/lang/1174719097/l50

I have some questions about combined verbs. Is there a particular word for these so I can do some googling myself?

I'm talking about stuff like 飛込む　落ち込む etc
but not just 込む, there's other ones like ～始まる ～終わる ～かける ～くる ～する 等
Pretty much I'm just curious how they work. Like how is なってきた different to なった

are there any more of these wordcombos I'm missing?