Breaking Linear Regression

What happens if we break the assumptions of linear regression for machine learning?
RESOURCES
[1] What do linear regression parameters mean: datascience.st...
[2] This has some good intuition that distinguishes applications of linear regression: stats.stackexc...
[3] Why should residuals be normally distributed? qr.ae/pvl91W
[4] Penn State's notes on the assumptions of linear regression: online.stat.ps...
[5]What do normal residuals tell you about your data: stats.stackexc...
[6] Wikipedia on linear regression (it's actually pretty good): en.wikipedia.o...
[7] Better understanding of "Linear in parameters": datascience.st...
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