This thesis focuses on the development of nonlinear optical techniques and the measurement of topological properties of the Weyl semimetals. The first portion of this thesis describes technical developments of the nonlinear optical spectroscopic probes rotational anisotropy second harmonic generation (RA-SHG) and transient grating. In our work on SHG, we describe a fast-reflective optic-based rotational anisotropy nonlinear harmonic generation spectrometer built upon synchronization of stepper motors and a voice-coil fast turning motor with data recorded by a data acquisition card. This device enables fast accumulation of significantly more data points than traditional SHG spectrometers and further allows spectral measurement over a broad wavelength range to be performed without optical realignment. We then describe the Fourier domain RA-SHG, allows direct measurements of the RA-SHG signal components of Cn symmetry. This method is based on the fast scanning RA-SHG device described above and operates by recording the nth harmonics of the fast scanning signal using a lock-in amplifier. Finally, we describe a novel method of performing transient grating measurements based on low power laser diodes, a laser diode pulser, a digital delay generator, and a data acquisition card. The RA-SHG technique was applied to the chiral Weyl semimetal RhSi, where a spectrum of the sole SHG tensor element χ(2) i jk was measured over the unprecedented 0.275-1.5 eV incoming photon energy range. Our data shows evidence of a strong surface state response and are detailed enough to reveal the second order corrections to the linear band structure as well as the Pauli blocking condition which was observed to occur at ∼630 meV. We also describe measurements of the linear photogalvanic effect (LPGE) and circular photogalvanic effect (CPGE) in RhSi deriving from topological Fermi arc states. While the magnitude of the CPGE response broadly matched theoretical predictions, the data also exhibit an inexplicably high degree of symmetry in the response as a function of incoming polarization in both CPGE and LPGE channels. Collaborative work on the SHG spectrum from TaAs is also described, from which we attribute the origin of the SHG response peak to the third cumulant of the Bloch wavefunction. Further collaborative studies of the CPGE in RhSi (111) revealed a response that was likely due to the topological band structure, but that also shows that the theoretically predicted quantized CPGE was not observed due to impurities and from contributions from sources other than the Weyl nodes. Finally, we briefly summarized how the crystal structure of PrAlGe1-xSix was revealed to be non-centrosymmetric using the RA-SHG technique. Transition from intrinsic to extrinsic anomalous Hall effect by tuning the dopant concentration x was studied in this ferromagnetic Weyl semimetal. / Physics