In the late 1960s, E.M. Landis made the following conjecture: If u and V are bounded functions, and u is a solution to the Schr\"odinger equation in Euclidean space that decays faster than exponential, then u must be identically zero. In 1992, V. Z. Meshkov disproved this conjecture by constructing bounded, complex-valued functions u and V that solve the Schr\"odinger equation in the plane and satisfy |u(x)| \le c \exp(- C |x|^{4/3}). The examples of Meshkov were accompanied by qualitative unique continuation estimates for solutions in any dimension. Meshkov's estimates were quantified in 2005 by J. Bourgain and C. Kenig. These results, and the generalizations that followed, have led to a fairly complete understanding of these unique continuation properties in the complex-valued setting. However, Landis' conjecture remained open in the real-valued setting. We will discuss a recent result of A. Logunov, E. Malinnikova, N. Nadirashvili, and F. Nazarov that resolves the real-valued version of Landis' conjecture in the plane, along with various generalizations.