This paper surveys the research on optimal consumption and investment problem of an agent who is subject to bankruptcy that has a specified utility (reward or penalty). The bankruptcy utility, modeled by a parameter, may be the result of welfare subsidies, the agent's innate ability to recover from bankruptcy, psychic costs associated with bankruptcy, etc. Models with nonnegative consumption, positive subsistence consumption, risky assets modeled by geometric Brownian motion or semimartingales are discussed. The paper concludes with suggestions for open research problems. This research is supported in part by SSHRC Grant 410-93-042. Filename: oci2.tex 1 1 Introduction This paper surveys the research on the optimal consumption-investment problem facing a utility maximizing agent (an individual or a household) that is subject to bankruptcy, the utility being associated with consumption and with bankruptcy. The problem has its beginning in the classical works of Phelps (1962), Ha..