Waveform or code design is an important topic in many applications, which has continu-ously attracted attention during the past several decades. The development of waveform design has been significantly advanced since the emergence of multiple-input multiple-output (MIMO) tech-nique. Compared to the single-waveform design for conventional radars, the multi-waveform design enables extra degrees of freedom (DOFs) for modern radars, which therefore triggers a series of rel-evant studies on MIMO radar. In this paper, we provide an overview on the main techniques of MIMO radar waveform designs developed in recent years, wherein the state-of-the-art methods are reviewed in terms of different designing criteria, including the minimization of auto- and cross-cor-relation levels (or equivalently, the integrated sidelobe level), the information theoretic, ambiguity function shaping, and signal-to-interference-plus-noise ratio maximization-based criteria, etc. Moreover, we give detailed comments on the main issues of different waveform designs, and also provide the possibly emerging directions toward the research on MIMO radar waveform design and potential challenges.