This survey highlights recent advances in numerical linear algebra algorithms using linear sketching. Sketching involves compressing a matrix with a random matrix to reduce computational complexity. The survey covers least squares regression, robust regression, low rank approximation, and graph sparsification. It discusses various problem variants and the limitations of sketching methods. The focus is on efficient algorithms that can handle large datasets by reducing the problem size through sketching. Key techniques include subspace embeddings, matrix multiplication, and leverage score sampling. The survey also addresses the trade-offs between accuracy, runtime, and data sparsity, showing how sketching can lead to faster and more scalable solutions for linear algebra problems.This survey highlights recent advances in numerical linear algebra algorithms using linear sketching. Sketching involves compressing a matrix with a random matrix to reduce computational complexity. The survey covers least squares regression, robust regression, low rank approximation, and graph sparsification. It discusses various problem variants and the limitations of sketching methods. The focus is on efficient algorithms that can handle large datasets by reducing the problem size through sketching. Key techniques include subspace embeddings, matrix multiplication, and leverage score sampling. The survey also addresses the trade-offs between accuracy, runtime, and data sparsity, showing how sketching can lead to faster and more scalable solutions for linear algebra problems.