Adhesives used to be such a simple consideration. "It's wood, so...errrrm...let's use wood glue."
Unfortunately, some minds far greater than mine have thrown this simplicity to the wind and given us more variety and choice for every application than ever before, making both repairs and creativity even more versitile and accessible, whatever the task or material at hand may be.
We do offer a word of caution here however. Some of these products can be irritants and caustic and should be treated with due care and respect to avoid hard or injury to yourself or others.