A linear measurement model is used to describe the measurement system where the measurements are linear combinations of the target signal. Due to its simplicity, it can be applied to various measurement systems. In this article, a comprehensive review of linear measurement model with a focus on optical systems is conducted by considering three different situations. Firstly, the assumption of signal sparsity is made, which turns the model into a compressive sensing problem. In spite of the various potentials demonstrated by the compressive sensing approach, it has been shown that compressive sensing is not fully ready for real-time applications yet due to its computational cost. Secondly, prior information of the target signal is taken into consideration to transform the linear measurement model into a linear manifold learning problem. With classical methods like principal component analysis (PCA), it has been demonstrated with two examples that such approach could simplify the measurement and the recovery process. Last but not least, the postprocessing step for the retrieval of information within the signal is further reduced through holistic design of the measurement system, granting systems with optical computation to make measurement faster and more robust against noise.