Renewable energy sources, such as wind and solar, are generally connected to the power system via voltage source inverters. These inverters typically operate in the grid-following mode to maximize their active power output without providing frequency support. Consequently, with the increasing penetration of renewable energy sources, the power system is experiencing a decline in frequency stability. To address this challenge, grid-forming inverters are emerging as a promising solution. Among various implementations of grid-forming inverters, the virtual synchronous generator excels for its capability to provide both primary frequency and inertia responses, which are achieved by emulating the behavior of conventional synchronous generators. Despite enhancing frequency stability, virtual synchronous generators may introduce low-frequency oscillations (LFOs), occurring either between different virtual synchronous generators or between virtual synchronous and synchronous generators. These oscillations can cause generators’ frequencies to temporarily deviate from the center-of-inertia frequency during transients, making the system frequency response models that assume a uniform frequency less accurate in frequency stability prediction. To address this problem, various modified virtual synchronous generator control schemes with enhanced LFO damping capabilities have been proposed in recent studies. This chapter provides a concise overview of these advancements. It first introduces the fundamental power stage and control mechanisms of virtual synchronous generators and evaluates their frequency stability enhancement capabilities using the system frequency response model. Subsequently, two virtual synchronous generator control schemes with improved LFO damping capability are introduced. The correctness of the theoretical findings and the effectiveness of the control schemes are demonstrated through simulations using a two-area power system model.