The issue of quantifying and characterizing various forms of social media manipulation and abuse has been at the forefront of the computational social science research community for over a decade. In this paper, I provide a (non-comprehensive) survey of research efforts aimed at estimating the prevalence of spam and false accounts on Twitter, as well as characterizing their use, activity, and behavior. I propose a taxonomy of spam and false accounts, enumerating known techniques used to create and detect them. Then, I summarize studies estimating the prevalence of spam and false accounts on Twitter. Finally, I report on research that illustrates how spam and false accounts are used for scams and frauds, stock market manipulation, political disinformation and deception, conspiracy amplification, coordinated influence, public health misinformation campaigns, radical propaganda and recruitment, and more. I will conclude with a set of recommendations aimed at charting the path forward to combat these problems.