The blockchain scalability problem refers to the discussion concerning the limits on the transaction throughput a blockchain network can process. It is related to the fact that records (known as blocks) in the bitcoin blockchain are limited in size and frequency .
From Bitcoin StackExchange: The term “on-chain scaling” is frequently used to exclusively refer to increasing the blockchain capacity by means of bigger blocks. However, in the literal sense of the term, it should refer to any sort of protocol change that improves the network’s capacity at the blockchain layer. These approaches tend to provide at most a linear capacity increase, although some are also scalability improvements .
- blocksize/blockweight increase;
- witness discount of segregated witness;
- smaller size of Schnorr signatures;
- Bellare-Neven signature aggregation;
- key aggregation.
From Tari Labs: Analogous to the OSI layers for communication, in blockchain technology decentralized Layer 2 protocols, also commonly referred to as Layer 2 scaling, refers to transaction throughput scaling solutions. Decentralized Layer 2 protocols run on top of the main blockchain (off-chain), while preserving the attributes of the main blockchain (e.g. crypto-economic consensus). Instead of each transaction, only the resultant of a number of transactions is embedded on-chain .
 Wikipedia: “Bitcoin Scalability Problem” [online]. Available: https://en.wikipedia.org/wiki/Bitcoin_scalability_problem. Date accessed: 2019‑06‑11.
 Bitcoin StackExchange: “What is the Difference between On-chain Scaling and Off-chain Scaling?” [online]. Available: https://bitcoin.stackexchange.com/questions/63375/what-is-the-difference-between-on-chain-scaling-and-off-chain-scaling. Date accessed: 2019‑06‑10.
“What is the Difference between On-chain Scaling and Off-chain Scaling?”
 Tari Labs: “Layer 2 Scaling Survey - What is Layer 2 Scaling?” [online]. Available: layer2scaling-landscape/layer2scaling-survey.html#what-is-layer-2-scaling. Date accessed: 2019‑06‑10.
“Layer 2 Scaling Survey - What is Layer 2 Scaling?”