Unlike the usual Nielsen complexity of a quantum mechanical system, the Krylov complexity (defined in 2019) is purely algorithmic for a countable quantum mechanical system, yet, despite being relatable to Nielsen complexity, a general holographic description for it was still lacking. Based on a proposal for AdS_3/CFT_2, we give a general formula, and consider 3 relevant cases: N=4 SYM, where we find a relation to an SL(2)-based spin chain (possibly related to the Krylov chain), confining systems exemplified by an asymptotically AdS_3 one, and a warped AdS_3/2 one, dual to a CFT quiver. The analysis of all other cases should follow along the lines of these ones.