The roadmap is an active area of research. The outline below is only intended to provide flavour. It is intended for this document to be maintained with ongoing R&D.
Sourced originally from the now retired spec for phase 1 sharding, with modifications.
Phase 1: Basic sharding without EVM
Phase 2: EVM state transition function
- Account abstraction
- Archive accumulators: https://ethresear.ch/t/history-state-and-asynchronous-accumulators-in-the-stateless-model/287 and https://ethresear.ch/t/batching-and-cyclic-partitioning-of-logs/536 and https://ethresear.ch/t/double-batched-merkle-log-accumulator/571
- Storage rent: here and here.
- Bandwidth fees
Phase 3: Light client state protocol
Phase 4: Cross-shard transactions: see here and more.
Phase 5: Tight coupling with main chain security: here and more.
- Data availability proofs: A note on data availability and erasure coding, https://ethresear.ch/t/sharding-and-data-forgetfulness/61,
- Casper integration.
- Internally fork-free sharding
- Manager shard
Phase 6: Super-quadratic or exponential sharding
- Recursively, shards within shards within shards...
- Load balancing: Wikipedia, search results. Related: https://ethresear.ch/t/history-state-and-asynchronous-accumulators-in-the-stateless-model/287, https://ethresear.ch/t/state-minimized-implementation-on-current-evm/1255
And a lot more: https://ethresear.ch/c/sharding.
- zk-STARKs, e.g. StarkWare the startup; videos here, here and here, as well as a paper here (the abstract is a more succinct intro than the videos), while the full paper is more detailed; and
- heterogeneous sharding