This paper reviews the progress in developing the LaxYySc4-x-y(BO3)4-LYSB and Yb-doped LaxYySc4-x-y(BO3)4-LYSB:Yb huntite-type crystals grown by the Czochralski method as new candidates for the next generation of nonlinear optical (NLO) and/or laser crystals. Considering the incongruent melting of these crystals, the initial compositions of the melt and the pulling and rotation rates were optimized. Additionally, a special thermal setup was engineered to grow LYSB-type crystals by the Czochralski crystal growth method. The chemical compositions of the LYSB and LYSB:Yb grown crystals were found to be La0.78Y0.32Sc2.90(BO3)4 and La0.78Y0.32Yb0.04Sc2.86(BO3)4, respectively. Therefore, for the LYSB:Yb crystal, the doping concentration of Yb3+ ions was considered to be 4 at.% with respect to the nonstoichiometric (La1-xYx)1.25Sc2.75(BO3)4 undoped compounds, i.e., LYSB:Yb (4 at.%). In terms of NLO properties, the obtained results demonstrate that LYSB and LYSB:Yb (4 at.%) crystals possess remarkable properties specific to huntite-type crystals. The main advantage of these crystals consists in the fact that they may be obtained with large dimensions and excellent optical quality by the Czochralski method, which recommends them as a new class of highly efficient crystals for different NLO applications, including second harmonic generation (SHG) of high-power or high-energy laser beams. The laser performances of the LYSB:Yb (4 at.%) crystal prove its favorable intrinsic properties to generate laser emissions in the 1 µm range with high efficiency. The efficient laser emission at ~1028 nm together with good NLO characteristics to convert its own emission into emission at ~514 nm via SHG make the LYSB:Yb (4 at.%) crystal a very promising active medium to be used in self-frequency doubling configuration.