The B-factories and Large Hadron Collider experiments have demonstrated the ability to observe and measure the properties of bottomonium mesons. In order to discover missing states it is useful to know their properties to develop a successful search strategy. To this end we calculate the masses and decay properties of excited bottomonium states. We use the relativized quark model to calculate the masses and wave functions and the P30 quark-pair creation model to calculate decay widths to open bottom. We also summarize results for radiative transitions, annihilation decays, hadronic transitions and production cross sections which are used to develop strategies to find these states. We find that the bb¯ system has a rich spectroscopy that we expect to be substantially extended by the LHC and e+e- experiments in the near future. Some of the most promising possibilities at the LHC are observing the χb(1,2)(3P), χb(1,2)(4P) and ηb(3S) states in γμ+μ- final states that proceed via radiative transitions through (nS) intermediate states and 1D3J and 2D3J into γγμ+μ- final states proceeding via 1P3J→1S31 and 2P3J→2S31 intermediate states respectively. Some of the most interesting possibilities in e+e- collisions are studying the 1D3J states via 4γ cascades starting with the (3S) and the 3P3J states in γγμ+μ- final states starting with the (4S) and proceeding via(nS) intermediate states. Completing the bottomonium spectrum is an important validation of lattice QCD calculations and a test of our understanding of bottomonium states in the context of the quark model.