Recent advances in the technologies related to quantum computing have allowed the achievement of the so-called "quantum supremacy" milestone.  In this talk, I will briefly recap this achievement, and address how it relates to progress towards practical applications of quantum computers to problems in physics, chemistry, machine learning, and related areas.  I will overview some of the promising algorithms in this area, such as hybrid quantum-classical algorithms and variational quantum eigensolvers (VQE), including challenges that remain in their successful implementation.  This will naturally lead to a discussion of the impact of errors and the road towards quantum error correction prior to full fault tolerance using methods such as quantum subspace expansions.