In short: Ethereum scales with rollups & data availability sampling. But what does that mean?

Firstly, I'll note that the Ethereum roadmap is evolving, so whatever you may have read is already out of date. Especially all the 2018/19 articles about sharding and "Ethereum 2.0" - yeah, those are obsolete. Here, I'll briefly describe the state of affairs in February 2022.

Rollups

Rollups are layer 2 chains that fully inherit Ethereum's security, decentralization, liquidity & network effect properties. Multiple rollups are live today, with application-specific rollups like dYdX, zkSync 1.x and Loopring mature & optimized already. Smart contract rollups like Optimism, Arbitrum and StarkNet are in their early stages and awaiting optimizations through 2022.

Optimized rollups today are capable of $0.10 transaction fees with up to 4,500 TPS. Certain highly optimized rollups like dYdX can even scale up to 12,000 TPS. The likes of dYdX, Immutable X and Loopring actually have zero gas fees for trades as it's abstracted from the user. But this is just the beginning. This is like smart contracts in 2016.

The next question becomes - how can we push rollups further?

1. Rollups and application developers themselves will continue to optimize. We have seen Optimism decrease transaction fees by 30% in January, with another 30% cut due soon. Arbitrum also cut their fees in January, with Arbitrum Nitro estimated to slash fees by 50%. This will continue throughout 2022. Aave developer Emilio describes how they have reduced transaction fees 10x to $0.16-$0.25 on optimistic rollups through optimizations. These are some examples - costs on rollups will continue to decrease over time as they mature.
2. Unlike L1s, rollups get cheaper the more activity there is. So as rollups mature, there's more activity, and token incentives, we'll see rollups get cheaper.

The Surge

The Surge are upgrades to Ethereum consists of multiple steps that will open the floodgates for rollups. First, we will have intermediate steps like EIP-4488 or blob-carrying transactions. These will drop transaction fees by 5 times or more, over and above the two points described above. At least one of these intermediate steps is likely to be implemented around the end of 2022.

The final stage for The Surge is danksharding - a data layer built specifically to accelerate rollups. This integrates data availability sampling, and ushers in a new paradigm for blockchains. With data availability sampling, the more decentralized your network is, the more capacity there is for rollups. As bandwidth improves and Ethereum decentralizes, capacity will continue to increase. Over the years, there'll be enough to have millions of TPS across rollups - enough so the whole concept of TPS and transaction fees melts away. We'll be sitting and laughing about the time we used to worry about gas fees. Danksharding will roll out over time, with the first steps likely happening in 2023.

Statelessness & zkEVM

With The Surge, rollups will have massive scale and ultra low transaction fees. But Ethereum L1 will still be expensive. This doesn't matter because the end users will all be on rollups. But Ethereum L1 will also scale, first through statelessness, and then several years down the line with zkEVM. Even then, the cheapest fees will continue to be on rollups, which is why most people will just use rollups.