%\vspace*{-2mm} Epoch of cosmic reionization (EoR) is a very important era for the transition of our Universe dark ages to full ionized universe. It is also a very important issue in the study of cosmology. However, until now there are lack of precise measurements of EoR. One of the problems is that the huge foreground noise usually overwhelms the EoR signal, thus it is difficult to resolve the real signal from the observational data. In this thesis, I study the kinetic Sunyaev-Zel'dovich effect (kSZ), the X-ray background during EoR, and their correlations with the 21 cm signal of neutral hydrogen. Since the correlations between different measurements could efficiently remove their uncorrelated noises, our studies would help to measure the EoR signal from the observations in the near future. Since the kSZ effect is proportional to the line-of-sight velocity, the kSZ-21 cm correlation suffers from cancellation at small angular scales. We thus focus on the correlation between the kSZ-squared field (kSZ²) and 21 cm signals (kSZ²-21 cm). We first build the 2-D distributions of kSZ effect and the 21 cm signals at different redshifts using the semi-numerical simulations (21CMFAST), then study the kSZ²-21 cm correlations together with their evolution with redshift. It is found that, when the global ionization fraction is low ($x_e\lesssim 0.7$), the kSZ² fluctuation is dominated by the rare ionized bubbles, that leads to an anti-correlation with the 21 cm signal. With $0.8\lesssim x_e<1$, the correlation is dominated by small pockets of neutral regions, leading to a positive correlation. However, at very high redshifts with $x_e<0.15$, the spin temperature fluctuations change the sign of the correlation from negative to positive, since weakly ionized regions can have strong 21 cm signals in this case. To extract this correlation, Wiener filtering is effective in removing large signals from the primary CMB anisotropy. The expected signal-to-noise ratios for a sim10-hour integration of upcoming Square Kilometer Array (SKA) data cross-correlated with maps from the current generation of CMB observatories with 3.4muK noise and $1.7^\prime$ beam over 100deg² are 51, 60, and 37 for $x_e=0.2$, 0.5, and 0.9, respectively. The X-ray sources during EoR, that might contribute to the X-ray background, are the X-ray binaries, the accreting nuclear black holes, and the shock heated interstellar medium. We use high resolution hydrodynamical and radiative transfer simulations to study the contribution of these high-z energetic sources to the X-ray background and its correlations with the 21 cm signal. We find that these X-ray sources contribute only sim5% of the unresolved X-ray background in the soft 0.5--2$\rm keV$ band and sim4% in the hard 2--8$\rm keV$ band. The same sources contribute to less than sim2% of the measured angular power spectrum of the X-ray background fluctuations. Thus it is impossible to study the EoR using only the X-ray background measurements. Using the redshift information of 21 cm signal, the correlation between X-ray background and 21 cm signal (Xray-21 cm) could be used to study the properties of the X-ray sources during the EoR. I find that Xray-21 cm correlations are positive during the early stages of reionization when most of hydrogen is neutral, while they become negative when the intergalactic medium gets highly ionized, with the transition from positive to negative depending on both the X-ray model and the scale under consideration. With SKA as the reference instrument for the 21cm experiment, the predicted signal-to-noise ratio for such correlations is $<1$ if the corresponding X-ray survey is only able to resolve and remove X-ray sources with observed flux $>10^{-15}\rm erg\cdot cm^{-2} \cdot s^{-1}$, while the cumulative signal-to-noise ratio at $x_e=0.5$ is $\sim 5$ if sources with observed flux $>10^{-17}\rm erg\cdot cm^{-2} \cdot s^{-1}$ are detected.