気が付く (to notice)

It's painful to go on living once you've realized that you yourself are a failure.

She doesn't realize she's done anything wrong.

She walked past without noticing me.

She didn't seem to notice it was me.

Only after she'd finished reading the book did she realize who had written it.

While repairing a broken radio, I realize all over again that I don't understand how circuits work.

She glanced at her watch and realized it was past five.

She didn't notice that one of her buttons wasn't fastened properly.