Quantum computer have the potential to solve classically intractable problems. However, realizing a universal quantum computer is challenging with current technology. Before having a fully-fledged quantum computer, a more realistic question is what we can do with current and near-term quantum hardware. In this talk, I will first review the quantum algorithms that are designed for near-term and fault-tolerant quantum computers and discuss the challenges and possibilities to realize quantum advantages. Then, I will propose to focus more on the early-fault tolerant era and discuss what we should do next to achieve quantum advantage.