I have this same question but I see that 6.4 years ago people were of the opinion that a lot of the best practices were still under development and included quite a bit of of trial and error. I'm assuming things have improved now and the genomics/informatics community can probably point out some of the more popular/standard pipelines that are in use today. So I have the same question again:
What Is The Best Pipeline For Human Whole Exome Sequencing in 2016?
Development and validation of a whole-exome sequencing test for simultaneous detection of point mutations, indels and copy-number alterations for precision cancer care
It all depends to the number of samples in question for which exome data is produced and what depth of coverage has they been subjected to.
Before any SNP calling is made thr processing of bam files is mostly done by gatk and I would still go by it. However if you do not have enough samples and you are also having medium depth in the lines of 70-80x then other algorithms should be used for the variant calls in this case. Plethora of tools are available.
Gatk works well with high depthand large number of samples but if you have less number of samples then it is advisable to use gatk for processing alignments but final call can be made on gatk processed aligned files with other variant callers.
If you are working in tumor and there are evidences that low infiltrating mutations might hamper the genome stability causing mutational aberrations that might lead to a tumoral evolution. I would go for something like Mutect2 in that case. Rest any tool that targets high frequency mutations can be used to call variants. I always preferred the marriage of gatk preprocessing followed with variant calling post processing the alignment with some targeted variant callers to provide much more reliable and true positive calls.
See these artiles to get the information:
VDAP-GUI: a user-friendly pipeline for variant discovery and annotation of raw next-generation sequencing data
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4754298/
MutAid: Sanger and NGS Based Integrated Pipeline for Mutation Identification, Validation and Annotation in Human Molecular Genetics
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4739551/
Evaluation of Next Generation Sequencing Platforms for Whole Exome Variant Analysis
http://www.omicsonline.org/open-access/evaluation-of-next-generation-sequencing-platforms-for-whole-exome-variant-analysis-2471-2663-1000112.pdf
This article below is from June 2015, but I don't think half a year really matters:
New insights into the performance of human whole-exome capture platforms
http://nar.oxfordjournals.org/content/early/2015/03/27/nar.gkv216.full
Development and validation of a whole-exome sequencing test for simultaneous detection of point mutations, indels and copy-number alterations for precision cancer care
http://www.nature.com/articles/npjgenmed201619
New tool mines whole-exome sequencing data to match cancer with best drug
https://www.sciencedaily.com/releases/2016/03/160329184959.htm
Unsolved challenges of clinical whole-exome sequencing: a systematic literature review of end-users’ views
https://bmcmedgenomics.biomedcentral.com/articles/10.1186/s12920-016-0213-6
Most advances are reported for new medical treatment.