The Arrhenius equation is an elementary treatment that gives the quantitative basis of the relationship between the activation energy and the reaction rate at which a reaction proceeds. The rate constant as a function of thermodynamic temperature is then given by:
The reaction rate is given by:
where E is the activation energy, and R is the gas constant, and m and n are experimentally determined partial orders in [A] and [B], respectively.  Since at temperature T the molecules have energies according to a Boltzmann distribution, one can expect the proportion of collisions with energy greater than E to vary with e. The constant of proportionality A is the pre-exponential factor, or frequency factor (not to be confused here with the reactant A) takes into consideration the frequency at which reactant molecules are colliding and the likelihood that a collision leads to a successful reaction.  Here, A has the same dimensions as an (m + n)-order rate constant (see Units below).
Another popular model that is derived using more sophisticated statistical mechanical considerations is the Eyring equation from transition state theory:
where ΔG is the free energy of activation, a parameter that incorporates both the enthalpy and entropy change needed to reach the transition state.  The temperature dependence of ΔG is used to compute these parameters, the enthalpy of activation ΔH and the entropy of activation ΔS, based on the defining formula ΔG = ΔH − TΔS.  In effect, the free energy of activation takes into account both the activation energy and the likelihood of successful collision, while the factor kT/h gives the frequency of molecular collision.    
The factor (c) ensures the dimensional correctness of the rate constant when the transition state in question is bimolecular or higher.  Here, c is the standard concentration, generally chosen based on the unit of concentration used (usually c = 1 mol L = 1 M), and M is the molecularity of the transition state.  Lastly, κ, usually set to unity, is known as the transmission coefficient, a parameter which essentially serves as a "fudge factor" for transition state theory.   
The biggest difference between the two theories is that Arrhenius theory attempts to model the reaction (single- or multi-step) as a whole, while transition state theory models the individual elementary steps involved.  Thus, they are not directly comparable, unless the reaction in question involves only a single elementary step.
Finally, in the past, collision theory, in which reactants are viewed as hard spheres with a particular cross-section, provided yet another common way to rationalize and model the temperature dependence of the rate constant, although this approach has gradually fallen into disuse.  The equation for the rate constant is similar in functional form to both the Arrhenius and Eyring equations:
where P is the steric (or probability) factor and Z is the collision frequency, and ΔE is energy input required to overcome the activation barrier.  Of note, , making the temperature dependence of k different from both the Arrhenius and Eyring models.