Solutions like sharding, off-chain transactions to increase Bitcoin's transaction capacity. Bitcoin's blockchain processes approximately 7 transactions per second. Scalability solutions aim to increase this capacity.
It theory, sharding will solve enhance Bitcoin scalability, but in practice, Bitcoin uses a simple UTXO model and a single-chain structure. Forcing the sharding solution on bitcoin will cause consensus issues. As also mentioned by ambatman, security which is a major pride of bitcoin could be compromised.
As for off-chain transaction, layer 2 solutions have been in play for sometime despite that it's not getting the desired adoption.