There are a lot of approaches to teaching 'grammar' for a second language. In this post I outline X number of positions that roughly lie along a spectrum
1. No grammar, pure induction
This would be the approach that teaches entirely in the target language, and avoids trying to draw any attention to grammatical features per se. A course or instructor may well be designing their course with all sorts of grammar in the background, but the main idea is to avoid any mention of it, and trust that the students will learn what things "sound/read correctly" by induction and exposure. Like many native speakers, they may become fluent speakers who cannot explain the grammar of the language (as, for instance, many English speakers are hopeless when confronted with ESL students' grammar questions)
2. Target language, minimal grammar
This approach involves instruction primarily in the target through communicative or similar methods, but features ad-hoc, "pop-up", or minimal grammar, as needed, and *taught in the target language*. The main goal is still communicative competency, but the value of pointing out grammar is seen and valued, while still practiced in the target language.
3. Target language, explicit grammar
A development of approach 2, this approach involves not only teaching the language communicatively, but teaching a full-orbed "grammar" of the language to students *still in the target language*. While approach 2 sees grammar as part of a means to an end, approach 3 sees ability to discourse *about the language in the language* as part of the goal.
4. Native language, minimal grammar
Similar to approach 2, but differing in that the teacher will revert back to the students' native language to explain grammar concepts. Such explanations are kept to a minimum, and designed to clarify quickly and accurately things that might be difficult in the target language.
5. Native language, post-inductive explicit grammar
Students are exposed first to native language material, generally designed to develop their abilities, and then are taught extensively and explicitly the grammar that the new material contains, in their native language. They may then review the target language content, with greater understanding from the explicit grammar. This is the approach taken in "inductive reading courses" when applied to classical languages.
6. Native language, deductive explicit grammar
This is the reverse order to 5, and in classical languages is exemplified by "grammar first, exercises second" textbooks of a more traditional mode. Grammar is taught explicitly, and predominantly, and then applied to the target language. Results with this method seem to involve students with strong knowledge of a target language's grammar, while often failing to have adequate communicative skills in that language
7. Native language, explicit grammar without target language instruction
This approach I would represent as "linguistic analysis without L2 acquisition". The main goal is to study or learn the linguistic structures of a language, not to acquire it in an active sense at all. Therefore all instruction is done in the native language, and provides a comprehensive analysis of a target language, with only examples and data sets presented in the target language.
Personally I favour an approach like number 3 for classical languages, since my goal is to provide an ability to engage in meta-discourse about texts, and explicit knowledge of grammar will aid that. If a student's goal is primarily communication/competency, for instance in a modern language, I would shift more towards approach 2.