The International Celestial Reference System (ICRS) now has realizations at several frequencies, all with an accuracy of several tens of mircoarcsecond ($\mathrm{\mu as}$) level, including the International Celestial Reference Frame (ICRF) based on observations of the very long baseline interferometry (VLBI) at S/X, K, and X/Ka band, and the Gaia celestial reference frame (Gaia-CRF) built by the Gaia mission.The link between the ICRF and Gaia-CRF is a non-trivial task for constructing a multiwavelength reference frame.It requires detailed analyses of the overall properties of both the ICRF and Gaia-CRF for the sake of deepening our understanding of these frames, which is of the main interest of this thesis. The first part is to investigate the internal and external accuracy of ICRF catalogs.The internal accuracy is estimated to range from $\mathrm{10\mu as}$ to $\mathrm{40\mu as}$, depending on the number of observations to individual sources.This analysis provides an independent validation to the documented value ($\mathrm{30\mu as}$) for the noise floor given by the ICRF3 Working Group, as well as indicates the potential accuracy VLBI catalogs could achieve.The external accuracy is studied by comparing all historic ICRF catalogs to the Gaia-CRF2 solution. The large-scale agreement is about $\mathrm{30\mu as}$ and $\mathrm{50\mu as}$ between the ICRF3 S/X band and K band and the Gaia-CRF2 catalogs.The X/Ka band catalog, however, presents deformations of about $\mathrm{200\mu as}$, indicating severe zonal errors in the X/Ka band frame.The possible method of improving the stability of the ICRF axes is also explored, in term of defining source selection.A new selection algorithm considering both source positional stability and uniformness of source distribution is proposed, which is supposed to improve the axis stability by a factor of two compared to the ICRF2. Secondly, different aspects related to the celestial frame in the Gaia Data Release 1 and 2 (DR1 and DR2) are concerned.The non-rotating of the stellar frame of the DR1 is investigated in the light of the global spin of Gaia-CRF1 with respect to the \textscHIPPARCOS frames and using Galactic kinematical analysis.Both methods yield possible residual rotation of around $\mathrm{0.3mas\cdot yr^{-1}}$ in the DR1 frame.As for the DR2, the magnitude-dependent error is estimated to have little influence on the global property of the Gaia-CRF2, suggesting that the overall accuracy of the Gaia-CRF might not degrade like the precision.It underlines a new aspect of the radio-to-optical frame link, which was thought to be taken place only among bright quasars. In preparation for the radio-to-optical frame link, the correlation between the radio-to-optical offsets and source properties are tested statistically to understand its origin.The radio-to-optical offset is found to correlate strongly with the magnitude, however, this correlation would diminish when one consider the position formal error.As a result, large offsets for faint sources are likely resulted from the magnitude-dependent error rather than astrophysical cause.Besides, a method of the radio-to-optical frame link is proposed, whose idea is to introduce the Gaia-CRF in the VLBI data analysis.The preliminary tests suggest no benefit to do so, but it should be re-tested based on the future Gaia data releases with improved accuracy. In conclusion, the agreement among the ICRF3 S/X band frame, K band frame, and Gaia-CRF2 is excellent.However, X/Ka band frame suffers from zonal errors and needs to be improved.More tests on the radio-to-optical frame-tie should be carried out based on the actual Gaia data.