While both 以后 (yǐhòu) and 后来 (hòulái) can mean "after," they have distinct uses.
以后 is used for the future in general
以后 is used when talking about things that happen at some unspecified point in the future.
Structure
Examples
他 以后 不 想 住 在 日本 。
以后 is used for things occurring after a specific time
以后 can be used to describe actions or events that occur after a specific time (and the time must be given).
Structure
Note that the time can be specific (like a date or time) or broad (like an event, action, or occurrence).
Examples
两 个 星期 以后,我 要 回 美国 。
后来 is used for sequencing past events
后来 is used to sequence two events that have already occurred. It is the Chinese equivalent of the English word "afterward".
Strucure
Examples
去年 我们 分手 了,后来 再 也 没 见 过 她。