In this chapter, we first introduce new requirements of 5G wireless network and its differences from past generations. The question "Why do we need new waveforms?" is answered in these respects. In the following sections, time-frequency (TF) lattice structure, pulse shaping, and multicarrier schemes are discussed in detail. TF lattice structures give information about TF localization of the pulse shape of employed filters. The structures are examined for multicarrier, single-carrier, time-division, and frequency-division multiplexing schemes, comparatively. Dispersion on time and frequency response of these filters may cause interference among symbols and carriers. Thus, effects of different pulse shapes, their corresponding transceiver structures, and trade-offs are given. Finally, performance evaluations of the selected waveform structures for 5G wireless communication systems are discussed.