The construction of the James Webb Space Telescope has brought attention to infrared astronomy and cosmology. The potential information about our universe to be gained by this mission and future infrared telescopes is staggering, but infrared observation faces many obstacles. These telescopes face large amounts of noise by many phenomena, from emission off of the mirrors to the cosmic infrared background. Infrared telescopes need to be designed in such a way that noise is minimized to achieve sufficient signal to noise ratio on high redshift objects. We will investigate current and planned space and ground based telescopes, model the noise they encounter, and discover their limitations. The ultimate goal of our investigation is to compare the sensitivity of these missions in the near and mid IR and to propose new missions. Our investigation is broken down into four major sections: current missions, noise, signal, and proposed missions. In the proposed missions section we investigate historical and current infrared telescopes with attention given to their location and properties. The noise section discusses the noise that an infrared telescope will encounter and set the background limit. The signal section will look at the spectral energy distributions (SED) of a few significant objects in our universe. We will calculate the intensity of the objects at various points on Earth and in orbit. In the final section we use our findings in the signal and noise sections to model integration times (observation time) for a variety of missions to achieve a given signal to noise ratio (SNR).