The possibility of building a computer that takes advantage of the most subtle nature of quantum physics has been driving a lot of research in atomic and solid state physics for some time. It is still not clear what physical system or systems can be used for this purpose. One possibility that has been attracting significant attention from researchers is to use the spin state of an electron confined in a semiconductor quantum dot. The electron spin is magnetic in nature, so it naturally is well isolated from electrical fluctuations that can a loss of quantum coherence. It can also be manipulated electrically, by taking advantage of the exchange interaction. In this work we describe several experiments we have done to study the electron spin properties of lateral quantum dots. We have developed lateral quantum dot devices based on the silicon metal-oxide-semiconductor transistor, and studied the physics of electrons confined in these quantum dots. We measured the electron spin excited state lifetime, which was found to be as long as 30 ms at the lowest magnetic fields that we could measure. We fabricated and characterized a silicon double quantum dot. Using this double quantum dot design, we fabricated devices which combined a silicon double quantum dot with a superconducting microwave resonator. The microwave resonator was found to be sensitive to two-dimensional electrons in the transistor channel, which we measured and characterized. We developed a new method for extracting information from random telegraph signals, which are produced when we observe thermal fluctuations of electrons in quantum dots. The new statistical method, based on the hidden Markov model, allows us to detect spin-dependent effects in such fluctuations even though we are not able to directly observe the electron spin. We use this analysis technique on data from two experiments involving gallium arsenide quantum dots and use it to measure spin-dependent tunneling rates. Our results advance the understanding of electron spin physics in lateral quantum dots, in silicon and in gallium arsenide.