Better way to do "echo $x | sed ..." and "echo $x | grep ..."

"Unless you assume a specific shell, there is no better way to do this than “pipe echo to tool” (or just a “tool” itself like expr); it is all you can really count on with the traditional Bourne shell and/or the POSIX shell. If you consider other shells, then there are some other built-in possibilities.

ksh has

extra patterns: ?(pattern-list), *(pattern-list), {n}(pattern-list), {n,m}(pattern-list), @(pattern-list), !(pattern-list);
the %P printf specifier to convert a extended regular expression into a pattern (and %R for extended regular expression to pattern);
the expr == pattern condition in [[ expr ]] tests;
the ${param/pattern/replacement} parameter expansion.

bash has

the extglob option to enable most of the extra patterns of ksh (no {n} and {n,m});
the expr == pattern condition (in [[ expr ]] tests);
the ${param/pattern/replacement} parameter expansion;
(in newer versions) the expr =~ extregexp condition (in [[ expr ]] tests) that can match against extended regular expressions

with parenthesized subexpressions and the BASH_REMATCH parameter, sed-style replacements could be done.

zsh has

its own extended patterns with the EXTENDED_GLOB option;
ksh-like extended patterns with the KSH_GLOB option;
the expr == pattern condition (in [[ expr ]] tests);
the ${pattern/pattern/replacement} parameter expansion;
the expr =~ extregexp condition (in [[ expr ]] tests) that can match against extended regular expressions,

it can use PCRE instead of plain extended regular expressions if the RE_MATCH_PCRE option is set,
with parenthesized subexpressions, the MATCH parameter, and the match parameter (or BASH_REMATCH with the BASH_REMATCH option set), sed-style replacements could be done;

the zsh/pcre module that offers pcre_compile, pcre_study, and pcre_match commands and the -pcre-match test condition (in [[ expr ]] tests);
the zsh/regex module that offers the -regex-match test condition (in [[ expr ]] tests)."

"A good posix compatible way for testing if a variable contains a pattern is:

test ${var##*foo*} || <do something>;

The syntax of the parameter expansion is:

${parameter##pattern}

where pattern is a shell pattern."