The k-deck of a string s is the multi-set of all length-k subsequences of s. We study an old question: for which k can all binary strings s of length n be reconstructed perfectly from just the information of their k-decks? For example, 1001 can be reconstructed uniquely from its 3-deck {100, 101, 101, 001}, but has the same 2-deck {10, 10, 11, 00, 01, 01} as 0110. We may also investigate variants of this problem for larger alphabets and permutations, and study connections to coding theory, trace reconstruction, graph reconstruction, and geometric reconstruction. No significant background is needed, though familiarity with algebraic and probabilistic combinatorics will be helpful.