Someone was able to brute-force its n-bit key in less than 2^(n-1) steps.

Someone was able to find a collision in less than 2^(k/2) steps (for a k-bit hash)

Someone found a collision, i.e., two pre-images x<>y that hash to the same image h( x ) = h( y )

Someone found a pre-image to a given image (i.e., the one-wayness has been broken)