TPS (Transactions Per Second) is also called "system throughput", that is, "the number of transactions that the system can process per second". The biggest problem with current blockchains is performance. The following figure shows the single-day maximum transaction volume (data before 2019/10/1) of some public chains. The data comes from

Name Data date Trading volume TPS Note
BitCoin 2017/12/14 490644 5.67875 The theoretical limit is 7
Ethereum 2018/01/04 1349890 15.6237 Waiting for the implementation of sharding technology
TRON 2019/07/22 5280790 61.1203
EOS 2018/11/10 11557159 133.7634 Claimed to be over a million
Conflux Mainnet is not online 3000-6000 Claimed up to 6000

According to statistics, for an ordinary computer with 13Mbps Internet connection, E5-1620@3.5GHz 4Core CPU, 16G memory, 512G SSD hard disk (250MB/s), the theoretical upper limit of TPS caused by network bandwidth is about 7,000 TPS The theoretical upper limit of TPS caused by hard disk file I/O is 50,000 TPS, and the theoretical upper limit of TPS caused by CPU processing capacity is approximately 50,000 TPS [Timestamp Capital: Sharding Research Report].
The existing single-chain structure has bottlenecks in single-node resources such as bandwidth, storage, and computing.
In order to improve the throughput of the blockchain system, blockchain technology and academic experts have proposed a variety of highperformance solutions.[China Academy of Information and Communication Technology:Blockchain White Paper(2018)]:

Type DAG Parallel Reduction of node number
Optimizing Layer Topology Framework Consensus
Security High High May reduce
Resource consumption Low Low Low
Scalability Well Well Average
Difficulty Relatively Hard Average Security Assurance Scheme is relatively hard
Performance High High Average
Examples IOTA

Current mainstream Inter-chain technologies include Notary schemes, Sidechains/relays, and Hash-locking.:

Classification Notary Sidechain/relays Hash-Locking
Inter-Blockchain Bi-directional Bi-directional/Uni-directional Bi-directional
Asset Exchange Support Support Support
Asset Transfer Support Support No Support
Trust Require the thirdparty No require No require
Type Protocol Technology Architecture Algorithm
Difficulty Average Hard Easy
Use Case Ripple BTC relay
Lightning network