The main obstacle in power scaling of the well-known Nd-doped lasers such as Nd:YVO4 is the thermal lensing effect. One of the proposed solutions to effectively alleviate this problem was based on the reduction of heating within the laser crystal. This was extensively investigated with the Nd:YVO4 crystal by pumping the laser at 914 nm instead of the standard pumping at 808 nm wavelength. In context of high power applications, the crystal of Nd:GdVO4 is an interesting alternative to the Nd:YVO4 as it offers the benefits of good spectral features (similar to Nd:YVO4) and much higher thermal conductivity. However, there is only one proof-of-principle work on continuous-wave (CW) Nd:GdVO4 laser using this pumping approach in which an output power of 3.35 W was reported. The full power scaling potential of the Nd:GdVO4 laser crystal to produce high output power has not been demonstrated to date. In this PhD thesis, I addressed this issue and investigated the high power operation of Nd:GdVO4 lasers under a new pumping wavelength of 912 nm. First, the thermal lensing behaviour of a 1063 nm Nd:GdVO4 was studied, both experimentally and by finite element analysis (FEA) method. The thermal lensing strength in Nd:GdVO4 laser under 912 nm pumping was significantly reduced when compared to the Nd:GdVO4 laser with 808 nm pumping or even Nd:YVO4 laser with 914 nm pumping. The next step of this research was focused on high power operation of Nd:GdVO4 lasers where we achieved 19.8 W of output power at 1063 nm. As a side work in the CW regime of operation, the possibility of discrete wavelength tuning and dual-wavelength operation of the Nd:GdVO4 laser were examined by using an intracavity birefringent filter. Discrete wavelength operation at four different wavelengths was demonstrated. Furthermore, for the first time we were able to demonstrate a dual-wavelength operation of the Nd:GdVO4 laser as a 1063 and 1071 nm wavelength pair. The last aspect of this PhD thesis was concentrated on generation of picosecond pulses. We were able to report on the first semiconductor saturable absorber mirror (SESAM) mode-locked (ML) Nd:GdVO4 laser with 912 nm pumping. The laser generated 10.14 W of average output power with the pulse width of 16 ps at the repetition rate of 85.2 MHz. To the best of our knowledge this is the highest average output power ever obtained from any of the SESAM mode-locked Nd-doped solid-state lasers that were pumped around 912 nm.