Where in the canon does the Buddha teach about mindfulness?

I wanted to know if someone could reference passages from the canon where the Buddha teaches about mindfulness. If such passages exist that is. I was wondering about it because terms and explanations surrounding mindfulness can sound very modern and almost technical at times, depending on who explains it. Has mindfulness, as practiced in this modern age, any roots in the original teachings of the Buddha (as taught by Himself), or did this arise in more recent times? E.g. Vietnamese Monk Thich Nanh Hanh's school of mindfulness is an entire sect devoted to the practice of mindfulness. But is there any canonical, textual evidence? I couldn't find anything. Thanks.