The turning-on of the Large Hadron Collider is the momentous milestone in our quest for new physics beyond the Standard Model. Soon, we will be presented with the task of detecting, identifying, and studying the possibly large parameter space of the underlying model. In this thesis, we will look at some possible extensions to the SM, their signatures at colliders, and possible search strategies to explore the new physics in a model-independent way. In chapter 2, we study the extended neutral gauge sector of the Littlest Higgs model at the 500 GeV e+e- collider using the fermion pair production and Higgs associate production channel. We find that these channels can provide an accurate determination of the fundamental parameters and thus allows the verification of the little Higgs mechanism designed to cancel the Higgs mass quadratic divergence. In chapter 3, we study the ATLAS supersymmetry searches proposed for the 14 TeV pp collider using the $\sim$ 70k models of the phenomenological Minimal Supersymmetric Model (pMSSM) moldel set, that have survived many theoretical and experimental constraints. Since pMSSM does not make any simplifying assumptions about its SUSY-breaking mechanism at high scale, this encompasses a broad class of Supersymmetric models. We find that even though these searches were optimized mostly for mSUGRA signals, they are relatively robust in observing the more general pMSSM models. For the case of models in which squarks and gluinos have mass below 1 TeV, essentially all of these models ($> 99\%$) were observable in at least one of these searches, with 1 $fb^{-1}$ of integrated luminosity allowing for an uncertainty of 50\% in the SM background. We found that 0-lepton searches are the most powerful searches, while searches with 1-2 leptons do not have coverage as good as has been shown for mSUGRA. We then study possible reasons why a model could not be observed. These difficult models mostly include those with long-lived charginos which lead to small Missing Tranverse Energy (MET) and models with squeezed spectra which lead to soft jets that fail the jet cuts. In chapter 4, we study similar searches that have been carried out by ATLAS at the 7 TeV LHC. We found that systematic uncertainty again plays an important role in determining the coverage of the searches. This is especially true for searches with a large SM background, such as $n$-jet 0 lepton searches. We study the implication of a null result from the 7 TeV LHC. We find that the degree of fine-tuning in the pMSSM depends on the prior in which we scan our 19-dimensional space, but overall it is not as large as in mSUGRA. We find that a null result at the 7 TeV with $10 fb^{-1}$ and 20\% systematic errors would imply a need for a higher energy e+e- machine than the 500 GeV ILC to study Supersymmetry. Continuing on along the line of Supersymmetry, in chapter 5 we explore the possibility of adding one more generation to the MSSM (4GMSSM). We find that the CP-odd A boson can be very light due to the contribution of the heavy 4th generation fermion loops while all other Higgs particles (including the CP-even {\it h}) are all quite heavy. The parameter $tan(\beta)$ is strongly constrained to be between 0.5 and 2 due to perturbativity requirements on Yukawa couplings. We study the electroweak constraints as well as collider signatures on the possibility of a light A of mass $\sim$115 GeV. As for an LHC discovery, we find that this light A can be seen in the standard 2-photon Higgs search channel with cross-section more than an order of magnitude greater than that of the SM Higgs. In the last two chapters, we study possible search strategies to explore the new physics in a model-independent way. In chapter 6, we attempt to show how one could be largely agnostic about the underlying model in exploring the complete kinematically-allowed parameter space of pair-produced color octet particles (with mass $m_{\tilde{g}}$) that each directly decay into two jets plus a neutral stable particle (with mass $m_{\tilde{B}}$) that would escape the detectors and appear as MET. The kinematics of this process can be completely described by two parameters $m_{\tilde {g}}$ and $m_{\tilde {B}}$ , and in particular their splitting determines the softness or hardness of jets from the decay products. In order to cover the whole parameter space, one would need separate searches for different regions. We show that optimizing the final cuts for every ($m_{\tilde {g}}$, $m_{\tilde {B}}$) point, and combining all searches, can extend the coverage significantly. Since this is just based on the kinematics of the decay, this result can be easily interpreted for any model with this decay topology. In chapter 7, we carry this model-independent approach further in jets plus missing energy searches, by proposing that one should bin the measured data (or simulated SM background) differentially in MET and $H_T$ (scalar sum of invisible energy) for each search, and use them to set limits on any model of interest. We demonstrate this technique by carrying out a search similar to that studied in chapter 6, with one added decay step for the color octet particle, mainly it decays to 2 jets and another particle (with mass $m_{\tilde {W}}$) and it in turn decays to the neutral stable particle and 2 jets. We study different kinematic regions and set bounds in this 3-dimensional parameter space ($m_{\tilde {g}}$, $m_{\tilde {W}}$, $m_{\tilde {B}}$).