in accordance with; according to; as X, then Y (e.g. as we age we gain wisdom, as wine matures it becomes more valuable, etc.)
マニュアルに従って作業を進めた。
I proceeded with the work in accordance with the manual.
規則に従って行動することが求められる。
Acting in accordance with the rules is required.
年齢を重ねるに従って知識と経験が積み上がっていく。
As one gets older, knowledge and experience accumulate.