One of the most well-developed applications of coherent interaction with atoms is atomic frequency standards and clocks. Atomic clocks find significant roles in a number of scientific and technological settings. State-of-the-art, laser-cooled, Cs-fountain microwave clocks have demonstrated impressive frequency measurement accuracy, with fractional uncertainties below the 10^-15 level. On the other hand, frequency standards based on optical transitions have made substantial steps forward over the last decade, benefiting from their high operational frequencies. An interesting approach to such an optical standard uses atomic strontium confined in an optical lattice. The tight atomic confinement allows for nearly complete elimination of Doppler and recoil-related effects which can otherwise trouble the precise atomic interrogation. At the same time, the optical lattice is designed to equally perturb the two electronic clock states so that the confinement introduces a net zero shift of the natural transition frequency. This thesis describes the design and realization of an optical frequency standard using ⁸⁷Sr confined in a 1-D optical lattice. Techniques for atomic manipulation and control are described, including two-stage laser cooling, proper design of atomic confinement in a lattice potential, and optical pumping techniques. With the development of an ultra-stable coherent laser light source, atomic spectral linewidths of the optical clock transition are observed below 2 Hz. High accuracy spectroscopy of the clock transition is carried out utilizing a femtosecond frequency comb referenced to the NIST-F1 Cs fountain. To explore the performance of an improved, spin-polarized Sr standard, a coherent optical phase transfer link is established between JILA and NIST. This enables remote comparison of the Sr standard against optical standards at NIST, such as the cold Ca standard. The high frequency stability of a Sr-Ca comparison (3 × 10^-16 at 200 s) is used to make measurements of Sr transition frequency shifts at the fractional frequency level below 10^-16. These systematic shifts are discussed in detail, resulting in a total uncertainty of the Sr clock frequency at 1.5 × 10^-16, smaller than that of the best Cs standards of the time. Considerations relevant for future performance improvements are also discussed.