Vてきた indicates continuation of an action or phenomenon from the past up to the present.
On the other hand, Vていく indicates continuation of an action or phenomenon from the present into the future. These are typically used with verbs which express change (e.g., 進む[proceed], 減る[decrease], 向上する[improve]).
カメラの技術はずいぶん進んできました。
Up to now, technology related to cameras has greatly advanced.
科学はこれからも進歩していくでしょう。
I believe science will continue to make progress like it has in the past.
Lesson 17-6「犬がこちらへ走って来ます。」
A dog is running toward me.
Lesson 17-6「アリさんは国で日本語を習って来ました。」
Ali learned Japanese in his country, and came to Japan.
