For anybody new or returning to SSS, check out SLIP-0039:
https://github.com/satoshilabs/slips/blob/master/slip-0039.m...One of the big downsides of SSS is that it’s very raw and you have to do a lot of legwork to make it actually useable. For instance, you can sss_combine any arbitrary polynomial coefficients and get a result, you don’t know if the reconstituted data is correct until you try to use it. Implementations can vary in the finite field chosen because SSS doesn't specify one, and not all are equal and they are not interchangeable (coefficients from one don’t work in another). Another issue is that it’s susceptible to collusion. It’s rightfully criticized for its shortcomings and the argument follows the don’t roll your own crypto vein. SSS is like handing a dev XOR and telling them “now go encrypt things”.
SLIP39 solves this by formalizing a protocol for handling SSS splits built atop standards for crypto key serialization (BIP-39). SLIP defines a standard finite field (used when interpreting the polynomial coefficients), SLIP shards are unique on each generation so parties with the same underlying SSS shard can’t compare mnemonics, they’re mnemonically serialized for humans, and they have a checksum and group index metadata which makes a more sane UX possible when combining. SLIP also describes a two layer setup so you can manage trust by cordoning people off into groups to help litigate collusion.