The forecasted restriction of lead containing materials in piezoelectric devices has created vast interest into the development of alternatives, i.e. lead-free systems. Since the discovery of improved properties, ferroelectric ceramics have dominated the commercial market for piezoelectric sensors, actuators and transducers. Relaxor ferroelectric single crystals are considered the premium piezoelectric materials, with high piezoelectric coefficients and low dielectric losses that enable them to be utilised in high-end applications, such as medical imaging ultrasounds. This review features the progress of lead-free single crystals that aim to replicate the remarkable piezoelectric properties that have been achieved in relaxor-PbTiO3 ferroelectric systems. Solid-state crystal growth (SSCG) has become a critical technique in the development of high-quality single crystals for such systems. SSCG is advantaged by its lower growth temperatures than conventional melt and solution growth techniques by producing crystals through a solid phase transformation of a polycrystalline matrix into a single crystal. This allows for higher chemical homogeneity and volatility control, while remaining a cost-effective growth method. The proposed theories of abnormal grain growth, which is the underlying mechanism that facilitates SSCG, will initially be discussed, followed by the challenges that must be controlled for continual high-quality single crystal growth. Given the correct polycrystalline microstructure and other processing parameters, large single crystals can be produced of incongruently melting systems that are unachievable using other techniques. This review provides a comparison of the state of the art of SSCG versus melt and solution growth techniques and concludes with the authors' proposed focused points to inspire further improvements to both single crystal growth and piezoelectric properties.