Taproot is coming in 2021-Nov, but its been worked on for the last couple of years. What are upcoming improvements to Bitcoin that are just being talked about or being tested?
Given Taproot is a soft fork and a consensus change I will assume you are interested in consensus changes rather than non-consensus changes. There are incremental privacy improvements being worked on in Bitcoin Core (e.g. transaction rebroadcasting, coin selection) that don't require consensus changes. In addition, there is a lot of work to do to take advantage of the scaling and privacy improvements that Taproot offers now that we know that Taproot will activate in November 2021. For example, the Bitcoin Core wallet (and other wallets) need to support custom scripts and MuSig as they are unlikely to do so by November. The Lightning Network implementations will also likely implement P2TR addresses, MuSig and PTLCs (point time locked contracts) at some point in the future though perhaps not before November. Antoine Riard discussed how the Lightning Network could change with Taproot in this presentation at Advancing Bitcoin 2020.
So there is a lot still to do to take advantage of Taproot. It is difficult to speculate on what will be included in the next soft fork let alone any future soft forks after that, I don't have a crystal ball.
Here are some of the candidates for what could be included in the next soft fork. It is not an exhaustive list and is in no particular order.
- Re-enable disabled opcodes like OP_CAT
- Extend existing math opcodes (ADD, MUL on 64-bit or 256-bit numbers)
- Commit to block hash at a given height (for replay protection against chain splits or reorgs)
- Changing the scripting language entirely (eg Simplicity)
- Graftroot or generalized Taproot
- Cross-input signature aggregation
If you are interested in more details for any of these refer to the StackExchange posts on these topics or if they do not exist feel free to create a new one :)