To go on living; to continue to live or subsist — often implies continuing one's life or making a living from now on.
これからどう生きていくかを真剣に考えている。
I'm seriously thinking about how to live from now on.
夢のために、どんな苦労をしても生きていくと決めた。
For the sake of my dream, I've decided to keep on living no matter the hardships.
親の期待に応えながら生きていくのは簡単ではない。
Living while meeting my parents' expectations is not easy.