  Multiple-input multiple-output (MIMO) systems are required to communicate
reliably at high spectral bands using a large number of antennas, while
operating under strict power and cost constraints. In order to meet these
constraints, future MIMO receivers are expected to operate with low resolution
quantizers, namely, utilize a limited number of bits for representing their
observed measurements, inherently distorting the digital representation of the
acquired signals. The fact that MIMO receivers use their measurements for some
task, such as symbol detection and channel estimation, other than recovering
the underlying analog signal, indicates that the distortion induced by
bit-constrained quantization can be reduced by designing the acquisition scheme
in light of the system task, i.e., by {\em task-based quantization}. In this
work we survey the theory and design approaches to task-based quantization,
presenting model-aware designs as well as data-driven implementations. Then, we
show how one can implement a task-based bit-constrained MIMO receiver,
presenting approaches ranging from conventional hybrid receiver architectures
to structures exploiting the dynamic nature of metasurface antennas. This
survey narrows the gap between theoretical task-based quantization and its
implementation in practice, providing concrete algorithmic and hardware design
principles for realizing task-based MIMO receivers.
